IOA/example/Lemmas.ML

--- a/IOA/example/Lemmas.ML	Fri Nov 11 10:35:03 1994 +0100
+++ b/IOA/example/Lemmas.ML	Mon Nov 21 17:50:34 1994 +0100
@@ -11,37 +11,37 @@
 (* Logic *)
 val prems = goal HOL.thy "(P ==> Q-->R) ==> P&Q --> R";
   by(fast_tac (HOL_cs addDs prems) 1);
-val imp_conj_lemma = result();
+qed "imp_conj_lemma";
 
 goal HOL.thy "(P --> (? x. Q(x))) = (? x. P --> Q(x))";
   by(fast_tac HOL_cs 1);
-val imp_ex_equiv = result();
+qed "imp_ex_equiv";
 
 goal HOL.thy "(A --> B & C) = ((A --> B) & (A --> C))";
   by (fast_tac HOL_cs 1);
-val fork_lemma = result();
+qed "fork_lemma";
 
 goal HOL.thy "((A --> B) & (C --> B)) = ((A | C) --> B)";
   by (fast_tac HOL_cs 1);
-val imp_or_lem = result();
+qed "imp_or_lem";
 
 goal HOL.thy "(X = (~ Y)) = ((~X) = Y)";
   by (fast_tac HOL_cs 1);
-val neg_flip = result();
+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);
-val imp_true_decompose = result();
+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);
-val imp_false_decompose = result();
+qed "imp_false_decompose";
 
 
 (* Sets *)
@@ -57,7 +57,7 @@
 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 = result() RS mp;
+val Suc_pred_lemma = store_thm("Suc_pred_lemma", result() RS mp);
 
 goal Arith.thy "x <= y --> x <= Suc(y)";
   by (rtac impI 1);
@@ -67,43 +67,43 @@
   by (etac disjE 1);
   by (etac less_SucI 1);
   by (asm_simp_tac nat_ss 1);
-val leq_imp_leq_suc = result() RS mp;
+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);
-val leq_suc = result();
+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);
-val left_plus_cancel = result();
+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);
-val left_plus_cancel_inside_succ = result();
+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);
-val nonzero_is_succ = result();
+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);
-val less_add_same_less = result();
+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);
-val leq_add_leq = result();
+qed "leq_add_leq";
 
 goal Arith.thy "(x::nat) + y <= z --> x <= z";
   by (nat_ind_tac "y" 1);
@@ -112,7 +112,7 @@
   by (rtac impI 1);
   by (dtac Suc_leD 1);
   by (fast_tac HOL_cs 1);
-val left_add_leq = result();
+qed "left_add_leq";
 
 goal Arith.thy "(A::nat) < B --> C < D --> A + C < B + D";
  by (rtac impI 1);
@@ -124,12 +124,12 @@
  by (res_inst_tac [("m1","B")] (add_commute RS ssubst) 1);
  by (rtac (less_add_same_less RS mp) 1);
  by (assume_tac 1);
-val less_add_cong = result();
+qed "less_add_cong";
 
 goal Nat.thy "!!i. [| i < j; j <= k |] ==> i < (k::nat)";
   by (dtac le_imp_less_or_eq 1);
   by (fast_tac (HOL_cs addIs [less_trans]) 1);
-val less_leq_less = result();
+qed "less_leq_less";
 
 goal Arith.thy "(A::nat) <= B --> C <= D --> A + C <= B + D";
   by (rtac impI 1);
@@ -145,7 +145,7 @@
   by (res_inst_tac [("m1","B")] (add_commute RS ssubst) 1);
   by (rtac (less_add_same_less RS mp) 1);
   by (assume_tac 1);
-val less_eq_add_cong = result();
+qed "less_eq_add_cong";
 
 goal Arith.thy "(w <= y) --> ((x::nat) + y <= z) --> (x + w <= z)";
   by (rtac impI 1); 
@@ -156,7 +156,7 @@
   by (rtac impI 1);
   by (etac le_trans 1);
   by (assume_tac 1);
-val leq_add_left_cong = result();
+qed "leq_add_left_cong";
 
 goal Arith.thy "(? x. y = Suc(x)) = (~(y = 0))";
   by (nat_ind_tac "y" 1);
@@ -164,7 +164,7 @@
   by (rtac iffI 1);
   by (asm_full_simp_tac arith_ss 1);
   by (fast_tac HOL_cs 1);
-val suc_not_zero = result();
+qed "suc_not_zero";
 
 goal Arith.thy "Suc(x) <= y --> (? z. y = Suc(z))";
   by (rtac impI 1);
@@ -176,7 +176,7 @@
   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);
-val suc_leq_suc = result();
+qed "suc_leq_suc";
 
 goal Arith.thy "~0<n --> n = 0";
   by (nat_ind_tac "n" 1);
@@ -184,43 +184,43 @@
   by (safe_tac HOL_cs);
   by (asm_full_simp_tac arith_ss 1);
   by (asm_full_simp_tac arith_ss 1);
-val zero_eq = result();
+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);
-val less_suc_imp_leq = result();
+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);
-val suc_pred_id = result();
+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);
-val pred_suc = result();
+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);
-val unzero_less = result();
+qed "unzero_less";
 
 (* Duplicate of earlier lemma! *)
 goal Arith.thy "x<(y::nat) --> y<=z --> x<(z::nat)";
   by (rtac impI 1); by (rtac impI 1);
   by (dtac  le_imp_less_or_eq 1);
   by (fast_tac (HOL_cs addIs [less_trans]) 1);
-val less_leq_less = result();
+qed "less_leq_less";
 
 goal Arith.thy "(Suc(n) <= Suc(m)) = (n <= m)";
   by (simp_tac (arith_ss addsimps [le_eq_less_or_eq]) 1);
-val succ_leq_mono = result();
+qed "succ_leq_mono";
 
 (* Odd proof. Why do induction? *)
 goal Arith.thy "((x::nat) = y + z) --> (y <= x)";
@@ -228,7 +228,7 @@
   by (simp_tac arith_ss 1);
   by (simp_tac (arith_ss addsimps 
                 [succ_leq_mono, le_refl RS (leq_add_leq RS mp)]) 1);
-val plus_leq_lem = result();
+qed "plus_leq_lem";
 
 (* Lists *)
 
@@ -236,20 +236,20 @@
   by (list_ind_tac "L" 1);
   by (simp_tac list_ss 1);
   by (asm_simp_tac list_ss 1);
-val append_cons = result();
+qed "append_cons";
 
 goal List.thy "(X ~= hd(L@M)) = (X ~= if(L = [], hd(M), hd(L)))";
   by (list_ind_tac "L" 1);
   by (simp_tac list_ss 1);
   by (asm_full_simp_tac list_ss 1);
-val not_hd_append = result();
+qed "not_hd_append";
 
 goal List.thy "(L = (x#rst)) --> (L = []) --> P";
   by (simp_tac list_ss 1);
-val list_cases = result();
+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);
-val cons_imp_not_null = result();
+qed "cons_imp_not_null";