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1 |
theory Term9
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imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove"
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begin
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4 |
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5 |
atom_decl name
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6 |
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7 |
datatype rlam9 =
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8 |
Var9 "name"
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9 |
| Lam9 "name" "rlam9" --"bind name in rlam"
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and rbla9 =
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Bla9 "rlam9" "rlam9" --"bind bv(first) in second"
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12 |
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13 |
primrec
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14 |
rbv9
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15 |
where
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16 |
"rbv9 (Var9 x) = {}"
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17 |
| "rbv9 (Lam9 x b) = {atom x}"
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18 |
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1277
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19 |
setup {* snd o define_raw_perms (Datatype.the_info @{theory} "Term9.rlam9") 2 *}
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print_theorems
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21 |
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1277
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22 |
local_setup {* snd o define_fv_alpha (Datatype.the_info @{theory} "Term9.rlam9") [
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[[[]], [[(NONE, 0)], [(NONE, 0)]]], [[[], [(SOME @{term rbv9}, 0)]]]] *}
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24 |
notation
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25 |
alpha_rlam9 ("_ \<approx>9l' _" [100, 100] 100) and
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alpha_rbla9 ("_ \<approx>9b' _" [100, 100] 100)
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thm alpha_rlam9_alpha_rbla9.intros
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28 |
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29 |
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inductive
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alpha9l :: "rlam9 \<Rightarrow> rlam9 \<Rightarrow> bool" ("_ \<approx>9l _" [100, 100] 100)
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32 |
and
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alpha9b :: "rbla9 \<Rightarrow> rbla9 \<Rightarrow> bool" ("_ \<approx>9b _" [100, 100] 100)
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34 |
where
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35 |
a1: "a = b \<Longrightarrow> (Var9 a) \<approx>9l (Var9 b)"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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36 |
| a4: "(\<exists>pi. (({atom x1}, t1) \<approx>gen alpha9l fv_rlam9 pi ({atom x2}, t2))) \<Longrightarrow> Lam9 x1 t1 \<approx>9l Lam9 x2 t2"
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37 |
| a3: "b1 \<approx>9l b2 \<Longrightarrow> (\<exists>pi. (((rbv9 b1), t1) \<approx>gen alpha9l fv_rlam9 pi ((rbv9 b2), t2))) \<Longrightarrow> Bla9 b1 t1 \<approx>9b Bla9 b2 t2"
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38 |
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39 |
quotient_type
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40 |
lam9 = rlam9 / alpha9l and bla9 = rbla9 / alpha9b
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41 |
sorry
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42 |
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43 |
local_setup {*
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44 |
(fn ctxt => ctxt
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45 |
|> snd o (Quotient_Def.quotient_lift_const ("qVar9", @{term Var9}))
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46 |
|> snd o (Quotient_Def.quotient_lift_const ("qLam9", @{term Lam9}))
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47 |
|> snd o (Quotient_Def.quotient_lift_const ("qBla9", @{term Bla9}))
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48 |
|> snd o (Quotient_Def.quotient_lift_const ("fv_lam9", @{term fv_rlam9}))
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49 |
|> snd o (Quotient_Def.quotient_lift_const ("fv_bla9", @{term fv_rbla9}))
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50 |
|> snd o (Quotient_Def.quotient_lift_const ("bv9", @{term rbv9})))
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51 |
*}
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52 |
print_theorems
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53 |
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54 |
instantiation lam9 and bla9 :: pt
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parents:
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55 |
begin
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56 |
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57 |
quotient_definition
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58 |
"permute_lam9 :: perm \<Rightarrow> lam9 \<Rightarrow> lam9"
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59 |
is
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60 |
"permute :: perm \<Rightarrow> rlam9 \<Rightarrow> rlam9"
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61 |
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62 |
quotient_definition
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63 |
"permute_bla9 :: perm \<Rightarrow> bla9 \<Rightarrow> bla9"
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64 |
is
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65 |
"permute :: perm \<Rightarrow> rbla9 \<Rightarrow> rbla9"
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66 |
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67 |
instance
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68 |
sorry
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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69 |
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70 |
end
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71 |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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72 |
lemma "\<lbrakk>b1 = b2; \<exists>pi. fv_lam9 t1 - bv9 b1 = fv_lam9 t2 - bv9 b2 \<and> (fv_lam9 t1 - bv9 b1) \<sharp>* pi \<and> pi \<bullet> t1 = t2\<rbrakk>
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73 |
\<Longrightarrow> qBla9 b1 t1 = qBla9 b2 t2"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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74 |
apply (lifting a3[unfolded alpha_gen])
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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75 |
apply injection
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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76 |
sorry
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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77 |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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78 |
end
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