equal
deleted
inserted
replaced
533 by (asm_full_simp_tac (simpset() addsimps [not_le_iff_lt,nat_into_Ord]) 1); |
533 by (asm_full_simp_tac (simpset() addsimps [not_le_iff_lt,nat_into_Ord]) 1); |
534 qed "add_le_elim1"; |
534 qed "add_le_elim1"; |
535 |
535 |
536 Goal "[| m<n; n: nat |] ==> EX k: nat. n = succ(m#+k)"; |
536 Goal "[| m<n; n: nat |] ==> EX k: nat. n = succ(m#+k)"; |
537 by (forward_tac [lt_nat_in_nat] 1 THEN assume_tac 1); |
537 by (forward_tac [lt_nat_in_nat] 1 THEN assume_tac 1); |
538 be rev_mp 1; |
538 by (etac rev_mp 1); |
539 by (induct_tac "n" 1); |
539 by (induct_tac "n" 1); |
540 by (ALLGOALS (simp_tac (simpset() addsimps [le_iff]))); |
540 by (ALLGOALS (simp_tac (simpset() addsimps [le_iff]))); |
541 by (blast_tac (claset() addSEs [leE] |
541 by (blast_tac (claset() addSEs [leE] |
542 addSIs [add_0_right RS sym, add_succ_right RS sym]) 1); |
542 addSIs [add_0_right RS sym, add_succ_right RS sym]) 1); |
543 qed_spec_mp "less_imp_Suc_add"; |
543 qed_spec_mp "less_imp_Suc_add"; |