diff -r f04b33ce250f -r a4dc62a46ee4 IOA/example/Lemmas.ML
--- a/IOA/example/Lemmas.ML	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,239 +0,0 @@
-(*  Title:      HOL/IOA/example/Lemmas.ML
-    ID:         $Id$
-    Author:     Tobias Nipkow & Konrad Slind
-    Copyright   1994  TU Muenchen
-
-(Mostly) Arithmetic lemmas
-Should realy go in Arith.ML.
-Also: Get rid of all the --> in favour of ==> !!!
-*)
-
-(* Logic *)
-val prems = goal HOL.thy "(P ==> Q-->R) ==> P&Q --> R";
-  by(fast_tac (HOL_cs addDs prems) 1);
-qed "imp_conj_lemma";
-
-goal HOL.thy "(P --> (? x. Q(x))) = (? x. P --> Q(x))";
-  by(fast_tac HOL_cs 1);
-qed "imp_ex_equiv";
-
-goal HOL.thy "(A --> B & C) = ((A --> B) & (A --> C))";
-  by (fast_tac HOL_cs 1);
-qed "fork_lemma";
-
-goal HOL.thy "((A --> B) & (C --> B)) = ((A | C) --> B)";
-  by (fast_tac HOL_cs 1);
-qed "imp_or_lem";
-
-goal HOL.thy "(X = (~ Y)) = ((~X) = Y)";
-  by (fast_tac HOL_cs 1);
-qed "neg_flip";
-
-goal HOL.thy "P --> Q(M) --> Q(if(P,M,N))";
-  by (rtac impI 1); 
-  by (rtac impI 1);
-  by (rtac (expand_if RS iffD2) 1);
-  by (fast_tac HOL_cs 1);
-qed "imp_true_decompose";
-
-goal HOL.thy "(~P) --> Q(N) --> Q(if(P,M,N))";
-  by (rtac impI 1); 
-  by (rtac impI 1);
-  by (rtac (expand_if RS iffD2) 1);
-  by (fast_tac HOL_cs 1);
-qed "imp_false_decompose";
-
-
-(* Sets *)
-val set_lemmas =
-   map (fn s => prove_goal Set.thy s (fn _ => [fast_tac set_cs 1]))
-        ["f(x) : (UN x. {f(x)})",
-         "f(x,y) : (UN x y. {f(x,y)})",
-         "!!a. (!x. a ~= f(x)) ==> a ~: (UN x. {f(x)})",
-         "!!a. (!x y. a ~= f(x,y)) ==> a ~: (UN x y. {f(x,y)})"];
-
-
-(* Arithmetic *)
-goal Arith.thy "n ~= 0 --> Suc(m+pred(n)) = m+n";
-  by (nat_ind_tac "n" 1);
-  by (REPEAT(simp_tac arith_ss 1));
-val Suc_pred_lemma = store_thm("Suc_pred_lemma", result() RS mp);
-
-goal Arith.thy "x <= y --> x <= Suc(y)";
-  by (rtac impI 1);
-  by (rtac (le_eq_less_or_eq RS iffD2) 1);
-  by (rtac disjI1 1);
-  by (dtac (le_eq_less_or_eq RS iffD1) 1);
-  by (etac disjE 1);
-  by (etac less_SucI 1);
-  by (asm_simp_tac nat_ss 1);
-val leq_imp_leq_suc = store_thm("leq_imp_leq_suc", result() RS mp);
-
-(* Same as previous! *)
-goal Arith.thy "(x::nat)<=y --> x<=Suc(y)";
-  by (simp_tac (arith_ss addsimps [le_eq_less_or_eq]) 1);
-qed "leq_suc";
-
-goal Arith.thy "((m::nat) + n = m + p) = (n = p)";
-  by (nat_ind_tac "m" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-qed "left_plus_cancel";
-
-goal Arith.thy "((x::nat) + y = Suc(x + z)) = (y = Suc(z))";
-  by (nat_ind_tac "x" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-qed "left_plus_cancel_inside_succ";
-
-goal Arith.thy "(x ~= 0) = (? y. x = Suc(y))";
-  by (nat_ind_tac "x" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-  by (fast_tac HOL_cs 1);
-qed "nonzero_is_succ";
-
-goal Arith.thy "(m::nat) < n --> m + p < n + p";
-  by (nat_ind_tac "p" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-qed "less_add_same_less";
-
-goal Arith.thy "(x::nat)<= y --> x<=y+k";
-  by (nat_ind_tac "k" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_full_simp_tac (arith_ss addsimps [leq_suc]) 1);
-qed "leq_add_leq";
-
-goal Arith.thy "(x::nat) + y <= z --> x <= z";
-  by (nat_ind_tac "y" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-  by (rtac impI 1);
-  by (dtac Suc_leD 1);
-  by (fast_tac HOL_cs 1);
-qed "left_add_leq";
-
-goal Arith.thy "(A::nat) < B --> C < D --> A + C < B + D";
- by (rtac impI 1);
- by (rtac impI 1);
- by (rtac less_trans 1);
- by (rtac (less_add_same_less RS mp) 1);
- by (assume_tac 1);
- by (rtac (add_commute RS ssubst)1);;
- by (res_inst_tac [("m1","B")] (add_commute RS ssubst) 1);
- by (rtac (less_add_same_less RS mp) 1);
- by (assume_tac 1);
-qed "less_add_cong";
-
-goal Arith.thy "(A::nat) <= B --> C <= D --> A + C <= B + D";
-  by (rtac impI 1);
-  by (rtac impI 1);
-  by (asm_full_simp_tac (arith_ss addsimps [le_eq_less_or_eq]) 1);
-  by (safe_tac HOL_cs);
-  by (rtac (less_add_cong RS mp RS mp) 1);
-  by (assume_tac 1);
-  by (assume_tac 1);
-  by (rtac (less_add_same_less RS mp) 1);
-  by (assume_tac 1);
-  by (rtac (add_commute RS ssubst)1);;
-  by (res_inst_tac [("m1","B")] (add_commute RS ssubst) 1);
-  by (rtac (less_add_same_less RS mp) 1);
-  by (assume_tac 1);
-qed "less_eq_add_cong";
-
-goal Arith.thy "(w <= y) --> ((x::nat) + y <= z) --> (x + w <= z)";
-  by (rtac impI 1); 
-  by (dtac (less_eq_add_cong RS mp) 1);
-  by (cut_facts_tac [le_refl] 1);
-  by (dres_inst_tac [("P","x<=x")] mp 1);by (assume_tac 1);
-  by (asm_full_simp_tac (HOL_ss addsimps [add_commute]) 1);
-  by (rtac impI 1);
-  by (etac le_trans 1);
-  by (assume_tac 1);
-qed "leq_add_left_cong";
-
-goal Arith.thy "(? x. y = Suc(x)) = (~(y = 0))";
-  by (nat_ind_tac "y" 1);
-  by (simp_tac arith_ss 1);
-  by (rtac iffI 1);
-  by (asm_full_simp_tac arith_ss 1);
-  by (fast_tac HOL_cs 1);
-qed "suc_not_zero";
-
-goal Arith.thy "Suc(x) <= y --> (? z. y = Suc(z))";
-  by (rtac impI 1);
-  by (asm_full_simp_tac (arith_ss addsimps [le_eq_less_or_eq]) 1);
-  by (safe_tac HOL_cs);
-  by (fast_tac HOL_cs 2);
-  by (asm_simp_tac (arith_ss addsimps [suc_not_zero]) 1);
-  by (rtac ccontr 1);
-  by (asm_full_simp_tac (arith_ss addsimps [suc_not_zero]) 1);
-  by (hyp_subst_tac 1);
-  by (asm_full_simp_tac arith_ss 1);
-qed "suc_leq_suc";
-
-goal Arith.thy "~0<n --> n = 0";
-  by (nat_ind_tac "n" 1);
-  by (asm_simp_tac arith_ss 1);
-  by (safe_tac HOL_cs);
-  by (asm_full_simp_tac arith_ss 1);
-  by (asm_full_simp_tac arith_ss 1);
-qed "zero_eq";
-
-goal Arith.thy "x < Suc(y) --> x<=y";
-  by (nat_ind_tac "n" 1);
-  by (asm_simp_tac arith_ss 1);
-  by (safe_tac HOL_cs);
-  by (etac less_imp_le 1);
-qed "less_suc_imp_leq";
-
-goal Arith.thy "0<x --> Suc(pred(x)) = x";
-  by (nat_ind_tac "x" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-qed "suc_pred_id";
-
-goal Arith.thy "0<x --> (pred(x) = y) = (x = Suc(y))";
-  by (nat_ind_tac "x" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-qed "pred_suc";
-
-goal Arith.thy "(x ~= 0) = (0<x)";
-  by (nat_ind_tac "x" 1);
-  by (simp_tac arith_ss 1);
-  by (asm_simp_tac arith_ss 1);
-qed "unzero_less";
-
-(* Odd proof. Why do induction? *)
-goal Arith.thy "((x::nat) = y + z) --> (y <= x)";
-  by (nat_ind_tac "y" 1);
-  by (simp_tac arith_ss 1);
-  by (simp_tac (arith_ss addsimps 
-                [Suc_le_mono, le_refl RS (leq_add_leq RS mp)]) 1);
-qed "plus_leq_lem";
-
-(* Lists *)
-
-goal List.thy "(xs @ (y#ys)) ~= []";
-  by (list.induct_tac "xs" 1);
-  by (simp_tac list_ss 1);
-  by (asm_simp_tac list_ss 1);
-qed "append_cons";
-
-goal List.thy "(x ~= hd(xs@ys)) = (x ~= if(xs = [], hd(ys), hd(xs)))";
-  by (list.induct_tac "xs" 1);
-  by (simp_tac list_ss 1);
-  by (asm_full_simp_tac list_ss 1);
-qed "not_hd_append";
-
-goal List.thy "(L = (x#rst)) --> (L = []) --> P";
-  by (simp_tac list_ss 1);
-qed "list_cases";
-
-goal List.thy "(? L2. L1 = x#L2) --> (L1 ~= [])";
-  by (strip_tac 1);
-  by (etac exE 1);
-  by (asm_simp_tac list_ss 1);
-qed "cons_imp_not_null";