equal
deleted
inserted
replaced
196 qed "wf_weak_decr_stable"; |
196 qed "wf_weak_decr_stable"; |
197 |
197 |
198 (* special case: <= *) |
198 (* special case: <= *) |
199 |
199 |
200 Goal "(m, n) : pred_nat^* = (m <= n)"; |
200 Goal "(m, n) : pred_nat^* = (m <= n)"; |
201 by (simp_tac (simpset() addsimps [less_eq, reflcl_trancl RS sym] |
201 by (simp_tac (simpset() addsimps [less_eq, thm"reflcl_trancl" RS sym] |
202 delsimps [reflcl_trancl]) 1); |
202 delsimps [thm"reflcl_trancl"]) 1); |
203 by (arith_tac 1); |
203 by (arith_tac 1); |
204 qed "le_eq"; |
204 qed "le_eq"; |
205 |
205 |
206 Goal "ALL i. f (Suc i) <= ((f i)::nat) ==> EX i. ALL k. f (i+k) = f i"; |
206 Goal "ALL i. f (Suc i) <= ((f i)::nat) ==> EX i. ALL k. f (i+k) = f i"; |
207 by (res_inst_tac [("r","pred_nat")] wf_weak_decr_stable 1); |
207 by (res_inst_tac [("r","pred_nat")] wf_weak_decr_stable 1); |