(* Title: HOLCF/IOA/meta_theory/Simulations.ML ID: $Id: Simulations.ML,v 1.9 2005/09/02 15:24:02 wenzelm Exp $ Author: Olaf Müller *) Goal "(A~={}) = (? x. x:A)"; by (safe_tac set_cs); by Auto_tac; qed"set_non_empty"; Goal "(A Int B ~= {}) = (? x. x: A & x:B)"; by (simp_tac (simpset() addsimps [set_non_empty]) 1); qed"Int_non_empty"; Goalw [Image_def] "(R``{x} Int S ~= {}) = (? y. (x,y):R & y:S)"; by (simp_tac (simpset() addsimps [Int_non_empty]) 1); qed"Sim_start_convert"; Addsimps [Sim_start_convert]; Goalw [is_ref_map_def,is_simulation_def] "!! f. is_ref_map f C A ==> is_simulation {p. (snd p) = f (fst p)} C A"; by (Asm_full_simp_tac 1); qed"ref_map_is_simulation";