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src/ZF/ex/Acc.ML

author | clasohm |

Thu Sep 16 12:20:38 1993 +0200 (1993-09-16) | |

changeset 0 | a5a9c433f639 |

child 95 | 2246a80b1cb5 |

permissions | -rw-r--r-- |

Initial revision

1 (* Title: ZF/ex/acc

2 ID: $Id$

3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory

4 Copyright 1993 University of Cambridge

6 Inductive definition of acc(r)

8 See Ch. Paulin-Mohring, Inductive Definitions in the System Coq.

9 Research Report 92-49, LIP, ENS Lyon. Dec 1992.

10 *)

12 structure Acc = Inductive_Fun

13 (val thy = WF.thy addconsts [(["acc"],"i=>i")];

14 val rec_doms = [("acc", "field(r)")];

15 val sintrs =

16 ["[| r-``{b} : Pow(acc(r)); b : field(r) |] ==> b : acc(r)"];

17 val monos = [Pow_mono];

18 val con_defs = [];

19 val type_intrs = [];

20 val type_elims = []);

22 goal Acc.thy "!!a b r. [| b: acc(r); <a,b>: r |] ==> a: acc(r)";

23 by (etac Acc.elim 1);

24 by (fast_tac ZF_cs 1);

25 val acc_downward = result();

27 val [major] = goal Acc.thy "field(r) <= acc(r) ==> wf(r)";

28 by (rtac (major RS wfI2) 1);

29 by (rtac subsetI 1);

30 by (etac Acc.induct 1);

31 by (etac (bspec RS mp) 1);

32 by (resolve_tac Acc.intrs 1);

33 by (assume_tac 2);

34 by (ALLGOALS (fast_tac ZF_cs));

35 val acc_wfI = result();

37 goal ZF.thy "!!r A. field(r Int A*A) <= field(r) Int A";

38 by (fast_tac ZF_cs 1);

39 val field_Int_prodself = result();

41 goal Acc.thy "wf(r Int (acc(r)*acc(r)))";

42 by (rtac (field_Int_prodself RS wfI2) 1);

43 by (rtac subsetI 1);

44 by (etac IntE 1);

45 by (etac Acc.induct 1);

46 by (etac (bspec RS mp) 1);

47 by (rtac IntI 1);

48 by (assume_tac 1);

49 by (resolve_tac Acc.intrs 1);

50 by (assume_tac 2);

51 by (ALLGOALS (fast_tac ZF_cs));

52 val wf_acc_Int = result();

54 val [major] = goal Acc.thy "wf(r) ==> field(r) <= acc(r)";

55 by (rtac subsetI 1);

56 by (etac (major RS wf_induct2) 1);

57 by (rtac subset_refl 1);

58 by (resolve_tac Acc.intrs 1);

59 by (assume_tac 2);

60 by (fast_tac ZF_cs 1);

61 val acc_wfD = result();

63 goal Acc.thy "wf(r) <-> field(r) <= acc(r)";

64 by (EVERY1 [rtac iffI, etac acc_wfD, etac acc_wfI]);

65 val wf_acc_iff = result();