author | fahadausaf <fahad.ausaf@icloud.com> |
Mon, 06 Oct 2014 16:42:52 +0100 | |
changeset 21 | 893f0314a88b |
parent 20 | c11651bbebf5 |
child 22 | fff2b8d356a5 |
thys/MyFirst.thy | file | annotate | diff | comparison | revisions |
--- a/thys/MyFirst.thy Mon Oct 06 15:24:41 2014 +0100 +++ b/thys/MyFirst.thy Mon Oct 06 16:42:52 2014 +0100 @@ -48,9 +48,6 @@ apply(auto) done -value "add 2 3" - - (**commutative-associative**) lemma add_04: "add m (add n k) = add (add m n) k" apply(induct m) @@ -58,10 +55,14 @@ done lemma add_zero: "add n 0 = n" -sorry +apply(induct n) +apply(auto) +done lemma add_Suc: "add m (Suc n) = Suc (add m n)" -sorry +apply(induct m) +apply(auto) +done lemma add_comm: "add m n = add n m" apply(induct m)