src/HOLCF/IOA/meta_theory/Simulations.ML
author kleing
Mon Jun 21 10:25:57 2004 +0200 (2004-06-21)
changeset 14981 e73f8140af78
parent 12525 4ad978c8f550
child 17233 41eee2e7b465
permissions -rw-r--r--
Merged in license change from Isabelle2004
mueller@4565
     1
(*  Title:      HOLCF/IOA/meta_theory/Simulations.ML
mueller@4565
     2
    ID:         $Id$
wenzelm@12218
     3
    Author:     Olaf Müller
mueller@4565
     4
wenzelm@12218
     5
Simulations in HOLCF/IOA.
mueller@4565
     6
*)
mueller@4565
     7
mueller@4565
     8
mueller@4565
     9
wenzelm@5068
    10
Goal "(A~={}) = (? x. x:A)";
mueller@4565
    11
by (safe_tac set_cs);
wenzelm@5132
    12
by Auto_tac;
mueller@4565
    13
qed"set_non_empty";
mueller@4565
    14
wenzelm@5068
    15
Goal "(A Int B ~= {}) = (? x. x: A & x:B)";
mueller@4565
    16
by (simp_tac (simpset() addsimps [set_non_empty]) 1);
mueller@4565
    17
qed"Int_non_empty";
mueller@4565
    18
mueller@4565
    19
wenzelm@5068
    20
Goalw [Image_def]
nipkow@10835
    21
"(R``{x} Int S ~= {}) = (? y. (x,y):R & y:S)";
mueller@4565
    22
by (simp_tac (simpset() addsimps [Int_non_empty]) 1);
mueller@4565
    23
qed"Sim_start_convert";
mueller@4565
    24
mueller@4565
    25
Addsimps [Sim_start_convert];
mueller@4565
    26
mueller@4565
    27
wenzelm@5068
    28
Goalw [is_ref_map_def,is_simulation_def]
mueller@4565
    29
"!! f. is_ref_map f C A ==> is_simulation {p. (snd p) = f (fst p)} C A";
mueller@4565
    30
by (Asm_full_simp_tac 1);
mueller@4565
    31
qed"ref_map_is_simulation";
mueller@4565
    32
mueller@4565
    33
mueller@4565
    34
mueller@4565
    35