| author | Christian Urban <christian dot urban at kcl dot ac dot uk> |
| Wed, 10 Jul 2013 17:47:30 +0100 | |
| changeset 381 | 99161cd17c0f |
| parent 62 | d94209ad2880 |
| permissions | -rw-r--r-- |
|
62
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
1 |
\begin{figure}[h!]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
2 |
\centering |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
3 |
\subfigure[First split]{\label{first_split}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
4 |
\scalebox{0.7}{
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
5 |
\begin{tikzpicture}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
6 |
\node[draw,minimum height=3.8ex] (xa) {$\hspace{2em}xa\hspace{2em}$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
7 |
\node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{5em}x - xa\hspace{5em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
8 |
\node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
9 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
10 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
11 |
(xa.north west) -- ($(xxa.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
12 |
node[midway, above=0.5em]{$x$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
13 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
14 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
15 |
(z.north west) -- ($(z.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
16 |
node[midway, above=0.5em]{$z$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
17 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
18 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
19 |
($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
20 |
node[midway, above=0.6em]{$x @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
21 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
22 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
23 |
($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
24 |
node[midway, below=0.5em]{$(x - xa) @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
25 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
26 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
27 |
($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
28 |
node[midway, below=0.5em]{$xa \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
29 |
\end{tikzpicture}}}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
30 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
31 |
\subfigure[Max split]{\label{max_split}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
32 |
\scalebox{0.7}{
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
33 |
\begin{tikzpicture}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
34 |
\node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}xa\_max\hspace{4em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
35 |
\node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}x - xa\_max\hspace{0.5em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
36 |
\node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
37 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
38 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
39 |
(xa.north west) -- ($(xxa.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
40 |
node[midway, above=0.5em]{$x$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
41 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
42 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
43 |
(z.north west) -- ($(z.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
44 |
node[midway, above=0.5em]{$z$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
45 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
46 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
47 |
($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
48 |
node[midway, above=0.8em]{$x @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
49 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
50 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
51 |
($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
52 |
node[midway, below=0.5em]{$(x - xa\_max) @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
53 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
54 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
55 |
($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
56 |
node[midway, below=0.5em]{$xa \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
57 |
\end{tikzpicture}}}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
58 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
59 |
\subfigure[Max split with $a$ and $b$ (the right situation)]{\label{ab_split}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
60 |
\scalebox{0.7}{
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
61 |
\begin{tikzpicture}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
62 |
\node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}xa\_max\hspace{4em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
63 |
\node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}x - xa\_max\hspace{0.5em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
64 |
\node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
65 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
66 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
67 |
(xa.north west) -- ($(xxa.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
68 |
node[midway, above=0.5em]{$x$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
69 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
70 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
71 |
(z.north west) -- ($(z.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
72 |
node[midway, above=0.5em]{$z$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
73 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
74 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
75 |
($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
76 |
node[midway, above=0.8em]{$x @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
77 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
78 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
79 |
($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
80 |
node[midway, below=0.5em]{$(x - xa\_max) @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
81 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
82 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
83 |
($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
84 |
node[midway, below=0.5em]{$xa \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
85 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
86 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
87 |
($(xxa.south east)+(6em,-5ex)$) -- ($(xxa.south west)+(0em,-5ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
88 |
node[midway, below=0.5em]{$a \in L_1$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
89 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
90 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
91 |
($(z.south east)+(0em,-5ex)$) -- ($(xxa.south east)+(6em,-5ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
92 |
node[midway, below=0.5em]{$b \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
93 |
\end{tikzpicture}}}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
94 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
95 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
96 |
\subfigure[Max split with $a$ and $b$ (the wrong situation)]{\label{ab_split_wrong}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
97 |
\scalebox{0.7}{
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
98 |
\begin{tikzpicture}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
99 |
\node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}xa\_max\hspace{4em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
100 |
\node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}x - xa\_max\hspace{0.5em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
101 |
\node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
102 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
103 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
104 |
(xa.north west) -- ($(xxa.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
105 |
node[midway, above=0.5em]{$x$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
106 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
107 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
108 |
(z.north west) -- ($(z.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
109 |
node[midway, above=0.5em]{$z$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
110 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
111 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
112 |
($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
113 |
node[midway, above=0.8em]{$x @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
114 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
115 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
116 |
($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
117 |
node[midway, below=0.5em]{$(x - xa\_max) @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
118 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
119 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
120 |
($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
121 |
node[midway, below=0.5em]{$xa \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
122 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
123 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
124 |
($(xxa.south east)+(-3em,-5ex)$) -- ($(xxa.south west)+(0em,-5ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
125 |
node[midway, below=0.5em]{$a \in L_1$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
126 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
127 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
128 |
($(z.south east)+(0em,-5ex)$) -- ($(xxa.south east)+(-3em,-5ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
129 |
node[midway, below=0.5em]{$b \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
130 |
\end{tikzpicture}}}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
131 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
132 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
133 |
\subfigure[Last split]{\label{last_split}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
134 |
\scalebox{0.7}{
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
135 |
\begin{tikzpicture}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
136 |
\node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}xa\_max\hspace{4em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
137 |
\node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}x - xa\_max\hspace{0.5em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
138 |
\node[draw,minimum height=3.8ex, right=-0.03em of xxa] (za) { $\hspace{2em}za\hspace{2em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
139 |
\node[draw,minimum height=3.8ex, right=-0.03em of za] (zb) { $\hspace{7em}zb\hspace{7em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
140 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
141 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
142 |
(xa.north west) -- ($(xxa.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
143 |
node[midway, above=0.5em]{$x$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
144 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
145 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
146 |
(za.north west) -- ($(zb.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
147 |
node[midway, above=0.5em]{$z$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
148 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
149 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
150 |
($(xa.north west)+(0em,3ex)$) -- ($(zb.north east)+(0em,3ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
151 |
node[midway, above=0.8em]{$x @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
152 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
153 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
154 |
($(za.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
155 |
node[midway, below=0.5em]{$(x - xa\_max) @ za \in L_1$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
156 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
157 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
158 |
($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
159 |
node[midway, below=0.5em]{$xa\_max \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
160 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
161 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
162 |
($(zb.south east)+(0em,0ex)$) -- ($(zb.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
163 |
node[midway, below=0.5em]{$zb \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
164 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
165 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
166 |
($(zb.south east)+(0em,-4ex)$) -- ($(xxa.south west)+(0em,-4ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
167 |
node[midway, below=0.5em]{$(x - xa\_max)@z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
168 |
\end{tikzpicture}}}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
169 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
170 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
171 |
\subfigure[Structure transferred to $y$]{\label{trans_split}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
172 |
\scalebox{0.7}{
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
173 |
\begin{tikzpicture}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
174 |
\node[draw,minimum height=3.8ex] (xa) { $\hspace{5em}ya\hspace{5em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
175 |
\node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{2em}y - ya\hspace{2em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
176 |
\node[draw,minimum height=3.8ex, right=-0.03em of xxa] (za) { $\hspace{2em}za\hspace{2em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
177 |
\node[draw,minimum height=3.8ex, right=-0.03em of za] (zb) { $\hspace{7em}zb\hspace{7em}$ };
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
178 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
179 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
180 |
(xa.north west) -- ($(xxa.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
181 |
node[midway, above=0.5em]{$y$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
182 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
183 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
184 |
(za.north west) -- ($(zb.north east)+(0em,0em)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
185 |
node[midway, above=0.5em]{$z$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
186 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
187 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
188 |
($(xa.north west)+(0em,3ex)$) -- ($(zb.north east)+(0em,3ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
189 |
node[midway, above=0.8em]{$y @ z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
190 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
191 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
192 |
($(za.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
193 |
node[midway, below=0.5em]{$(y - ya) @ za \in L_1$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
194 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
195 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
196 |
($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
197 |
node[midway, below=0.5em]{$ya \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
198 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
199 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
200 |
($(zb.south east)+(0em,0ex)$) -- ($(zb.south west)+(0em,0ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
201 |
node[midway, below=0.5em]{$zb \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
202 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
203 |
\draw[decoration={brace,transform={yscale=3}},decorate]
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
204 |
($(zb.south east)+(0em,-4ex)$) -- ($(xxa.south west)+(0em,-4ex)$) |
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
205 |
node[midway, below=0.5em]{$(y - ya)@z \in L_1*$};
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
206 |
\end{tikzpicture}}}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
207 |
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
208 |
\caption{The case for $STAR$}
|
|
d94209ad2880
Copy Myhill.thy into Myhill_2.thyand put Myhill_2.thy into logic ListP. Myhill.thy is now almost empty ready to be extended by new manuscripts.
zhang
parents:
diff
changeset
|
209 |
\end{figure}
|