diff -r 9f1eaab75e8c -r 771b1f6422a8 src/ZF/ex/Mutil.ML --- a/src/ZF/ex/Mutil.ML Mon Nov 03 12:22:43 1997 +0100 +++ b/src/ZF/ex/Mutil.ML Mon Nov 03 12:24:13 1997 +0100 @@ -23,22 +23,22 @@ bind_thm("Finite_evnodd", evnodd_subset RS subset_imp_lepoll RS lepoll_Finite); goalw thy [evnodd_def] "evnodd(A Un B, b) = evnodd(A,b) Un evnodd(B,b)"; -by (simp_tac (!simpset addsimps [Collect_Un]) 1); +by (simp_tac (simpset() addsimps [Collect_Un]) 1); qed "evnodd_Un"; goalw thy [evnodd_def] "evnodd(A - B, b) = evnodd(A,b) - evnodd(B,b)"; -by (simp_tac (!simpset addsimps [Collect_Diff]) 1); +by (simp_tac (simpset() addsimps [Collect_Diff]) 1); qed "evnodd_Diff"; goalw thy [evnodd_def] "evnodd(cons(,C), b) = \ \ if((i#+j) mod 2 = b, cons(, evnodd(C,b)), evnodd(C,b))"; -by (asm_simp_tac (!simpset addsimps [evnodd_def, Collect_cons] +by (asm_simp_tac (simpset() addsimps [evnodd_def, Collect_cons] setloop split_tac [expand_if]) 1); qed "evnodd_cons"; goalw thy [evnodd_def] "evnodd(0, b) = 0"; -by (simp_tac (!simpset addsimps [evnodd_def]) 1); +by (simp_tac (simpset() addsimps [evnodd_def]) 1); qed "evnodd_0"; Addsimps [evnodd_cons, evnodd_0]; @@ -46,7 +46,7 @@ (*** Dominoes ***) goal thy "!!d. d:domino ==> Finite(d)"; -by (blast_tac (!claset addSIs [Finite_cons, Finite_0] addEs [domino.elim]) 1); +by (blast_tac (claset() addSIs [Finite_cons, Finite_0] addEs [domino.elim]) 1); qed "domino_Finite"; goal thy "!!d. [| d:domino; b<2 |] ==> EX i' j'. evnodd(d,b) = {}"; @@ -55,9 +55,9 @@ by (res_inst_tac [("k1", "i#+j")] (mod2_cases RS disjE) 1); by (REPEAT_FIRST (ares_tac [add_type])); (*Four similar cases: case (i#+j) mod 2 = b, 2#-b, ...*) -by (REPEAT (asm_simp_tac (!simpset addsimps [mod_succ, succ_neq_self] +by (REPEAT (asm_simp_tac (simpset() addsimps [mod_succ, succ_neq_self] setloop split_tac [expand_if]) 1 - THEN blast_tac (!claset addDs [ltD]) 1)); + THEN blast_tac (claset() addDs [ltD]) 1)); qed "domino_singleton"; @@ -68,51 +68,51 @@ goal thy "!!t. t: tiling(A) ==> \ \ u: tiling(A) --> t Int u = 0 --> t Un u : tiling(A)"; by (etac tiling.induct 1); -by (simp_tac (!simpset addsimps tiling.intrs) 1); -by (asm_full_simp_tac (!simpset addsimps [Un_assoc, +by (simp_tac (simpset() addsimps tiling.intrs) 1); +by (asm_full_simp_tac (simpset() addsimps [Un_assoc, subset_empty_iff RS iff_sym]) 1); -by (blast_tac (!claset addIs tiling.intrs) 1); +by (blast_tac (claset() addIs tiling.intrs) 1); qed_spec_mp "tiling_UnI"; goal thy "!!t. t:tiling(domino) ==> Finite(t)"; by (eresolve_tac [tiling.induct] 1); by (resolve_tac [Finite_0] 1); -by (blast_tac (!claset addSIs [Finite_Un] addIs [domino_Finite]) 1); +by (blast_tac (claset() addSIs [Finite_Un] addIs [domino_Finite]) 1); qed "tiling_domino_Finite"; goal thy "!!t. t: tiling(domino) ==> |evnodd(t,0)| = |evnodd(t,1)|"; by (eresolve_tac [tiling.induct] 1); -by (simp_tac (!simpset addsimps [evnodd_def]) 1); +by (simp_tac (simpset() addsimps [evnodd_def]) 1); by (res_inst_tac [("b1","0")] (domino_singleton RS exE) 1); by (Simp_tac 2 THEN assume_tac 1); by (res_inst_tac [("b1","1")] (domino_singleton RS exE) 1); by (Simp_tac 2 THEN assume_tac 1); by (Step_tac 1); by (subgoal_tac "ALL p b. p:evnodd(a,b) --> p~:evnodd(ta,b)" 1); -by (asm_simp_tac (!simpset addsimps [evnodd_Un, Un_cons, tiling_domino_Finite, +by (asm_simp_tac (simpset() addsimps [evnodd_Un, Un_cons, tiling_domino_Finite, evnodd_subset RS subset_Finite, Finite_imp_cardinal_cons]) 1); -by (blast_tac (!claset addSDs [evnodd_subset RS subsetD] addEs [equalityE]) 1); +by (blast_tac (claset() addSDs [evnodd_subset RS subsetD] addEs [equalityE]) 1); qed "tiling_domino_0_1"; goal thy "!!i n. [| i: nat; n: nat |] ==> {i} * (n #+ n) : tiling(domino)"; by (nat_ind_tac "n" [] 1); -by (simp_tac (!simpset addsimps tiling.intrs) 1); -by (asm_simp_tac (!simpset addsimps [Un_assoc RS sym, Sigma_succ2]) 1); +by (simp_tac (simpset() addsimps tiling.intrs) 1); +by (asm_simp_tac (simpset() addsimps [Un_assoc RS sym, Sigma_succ2]) 1); by (resolve_tac tiling.intrs 1); by (assume_tac 2); by (subgoal_tac (*seems the easiest way of turning one to the other*) "{i}*{succ(n1#+n1)} Un {i}*{n1#+n1} = {, }" 1); by (Blast_tac 2); -by (asm_simp_tac (!simpset addsimps [domino.horiz]) 1); -by (blast_tac (!claset addEs [mem_irrefl, mem_asym]) 1); +by (asm_simp_tac (simpset() addsimps [domino.horiz]) 1); +by (blast_tac (claset() addEs [mem_irrefl, mem_asym]) 1); qed "dominoes_tile_row"; goal thy "!!m n. [| m: nat; n: nat |] ==> m * (n #+ n) : tiling(domino)"; by (nat_ind_tac "m" [] 1); -by (simp_tac (!simpset addsimps tiling.intrs) 1); -by (asm_simp_tac (!simpset addsimps [Sigma_succ1]) 1); -by (blast_tac (!claset addIs [tiling_UnI, dominoes_tile_row] +by (simp_tac (simpset() addsimps tiling.intrs) 1); +by (asm_simp_tac (simpset() addsimps [Sigma_succ1]) 1); +by (blast_tac (claset() addIs [tiling_UnI, dominoes_tile_row] addEs [mem_irrefl]) 1); qed "dominoes_tile_matrix"; @@ -124,23 +124,23 @@ by (resolve_tac [notI] 1); by (dresolve_tac [tiling_domino_0_1] 1); by (subgoal_tac "|evnodd(t',0)| < |evnodd(t',1)|" 1); -by (asm_full_simp_tac (!simpset addsimps [lt_not_refl]) 1); +by (asm_full_simp_tac (simpset() addsimps [lt_not_refl]) 1); by (subgoal_tac "t : tiling(domino)" 1); (*Requires a small simpset that won't move the succ applications*) by (asm_simp_tac (ZF_ss addsimps [nat_succI, add_type, dominoes_tile_matrix]) 2); by (subgoal_tac "(m#+m)#+(n#+n) = (m#+n)#+(m#+n)" 1); -by (asm_simp_tac (!simpset addsimps add_ac) 2); +by (asm_simp_tac (simpset() addsimps add_ac) 2); by (asm_full_simp_tac - (!simpset addsimps [evnodd_Diff, mod2_add_self, + (simpset() addsimps [evnodd_Diff, mod2_add_self, mod2_succ_succ, tiling_domino_0_1 RS sym]) 1); by (resolve_tac [lt_trans] 1); by (REPEAT (rtac Finite_imp_cardinal_Diff 1 THEN - asm_simp_tac (!simpset addsimps [tiling_domino_Finite, Finite_evnodd, + asm_simp_tac (simpset() addsimps [tiling_domino_Finite, Finite_evnodd, Finite_Diff]) 1 THEN - asm_simp_tac (!simpset addsimps [evnodd_iff, nat_0_le RS ltD, + asm_simp_tac (simpset() addsimps [evnodd_iff, nat_0_le RS ltD, mod2_add_self]) 1)); qed "mutil_not_tiling";