src/HOLCF/IOA/meta_theory/Simulations.ML
author nipkow
Tue Jan 09 15:36:30 2001 +0100 (2001-01-09)
changeset 10835 f4745d77e620
parent 10798 0a1446ff6aff
child 12218 6597093b77e7
permissions -rw-r--r--
` -> $
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(*  Title:      HOLCF/IOA/meta_theory/Simulations.ML
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    ID:         $Id$
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    Author:     Olaf Mueller
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    Copyright   1997  TU Muenchen
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Simulations in HOLCF/IOA
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*)
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Goal "(A~={}) = (? x. x:A)";
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by (safe_tac set_cs);
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by Auto_tac;
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qed"set_non_empty";
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Goal "(A Int B ~= {}) = (? x. x: A & x:B)";
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by (simp_tac (simpset() addsimps [set_non_empty]) 1);
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qed"Int_non_empty";
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Goalw [Image_def]
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"(R``{x} Int S ~= {}) = (? y. (x,y):R & y:S)";
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by (simp_tac (simpset() addsimps [Int_non_empty]) 1);
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qed"Sim_start_convert";
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Addsimps [Sim_start_convert];
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Goalw [is_ref_map_def,is_simulation_def]
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"!! f. is_ref_map f C A ==> is_simulation {p. (snd p) = f (fst p)} C A";
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(* start states *)
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by (Asm_full_simp_tac 1);
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(* main case *)
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by (Blast_tac 1);
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qed"ref_map_is_simulation";
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