# HG changeset patch # User paulson # Date 955631977 -7200 # Node ID 483a3eb96c7e5650a53a5a1c63c7d720f8e1e29d # Parent 2f2d2b4215d60e07648716199bf386d4b0c96dd8 stopped using the obsolete "nat_ind_tac" diff -r 2f2d2b4215d6 -r 483a3eb96c7e src/HOL/RelPow.ML --- a/src/HOL/RelPow.ML Thu Apr 13 15:18:02 2000 +0200 +++ b/src/HOL/RelPow.ML Thu Apr 13 15:19:37 2000 +0200 @@ -21,7 +21,7 @@ qed "rel_pow_Suc_I"; Goal "!z. (x,y) : R --> (y,z):R^n --> (x,z):R^(Suc n)"; -by (nat_ind_tac "n" 1); +by (induct_tac "n" 1); by (Simp_tac 1); by (Asm_full_simp_tac 1); by (Blast_tac 1); @@ -51,7 +51,7 @@ qed "rel_pow_E"; Goal "!x z. (x,z):R^(Suc n) --> (? y. (x,y):R & (y,z):R^n)"; -by (nat_ind_tac "n" 1); +by (induct_tac "n" 1); by (blast_tac (claset() addIs [rel_pow_0_I] addEs [rel_pow_0_E,rel_pow_Suc_E]) 1); by (blast_tac (claset() addIs [rel_pow_Suc_I] @@ -60,7 +60,7 @@ Goal "!x y z. (x,y) : R^n & (y,z) : R --> (? w. (x,w) : R & (w,z) : R^n)"; -by (nat_ind_tac "n" 1); +by (induct_tac "n" 1); by (ALLGOALS Asm_simp_tac); by (Blast_tac 1); qed_spec_mp "rel_pow_Suc_D2'"; @@ -89,7 +89,7 @@ qed "rtrancl_imp_UN_rel_pow"; Goal "!y. (x,y):R^n --> (x,y):R^*"; -by (nat_ind_tac "n" 1); +by (induct_tac "n" 1); by (blast_tac (claset() addIs [rtrancl_refl] addEs [rel_pow_0_E]) 1); by (blast_tac (claset() addEs [rel_pow_Suc_E] addIs [rtrancl_into_rtrancl]) 1); diff -r 2f2d2b4215d6 -r 483a3eb96c7e src/HOL/Univ.ML --- a/src/HOL/Univ.ML Thu Apr 13 15:18:02 2000 +0200 +++ b/src/HOL/Univ.ML Thu Apr 13 15:19:37 2000 +0200 @@ -214,7 +214,7 @@ qed "ndepth_K0"; Goal "k < Suc(LEAST x. f x = Inr 0) --> nat_case (Inr (Suc i)) f k ~= Inr 0"; -by (nat_ind_tac "k" 1); +by (induct_tac "k" 1); by (ALLGOALS Simp_tac); by (rtac impI 1); by (etac not_less_Least 1);