|
2019
|
1 |
(* Title: Option.ML
|
|
|
2 |
ID: $Id$
|
|
|
3 |
Author: Tobias Nipkow
|
|
|
4 |
Copyright 1996 TU Muenchen
|
|
|
5 |
|
|
|
6 |
Derived rules
|
|
|
7 |
*)
|
|
|
8 |
|
|
|
9 |
open Option;
|
|
|
10 |
|
|
|
11 |
val [prem] = goal Option.thy "P(opt) ==> P(None) | (? x. P(Some(x)))";
|
|
|
12 |
br (prem RS rev_mp) 1;
|
|
|
13 |
by (option.induct_tac "opt" 1);
|
|
|
14 |
by (ALLGOALS(Fast_tac));
|
|
|
15 |
bind_thm("optionE", standard(result() RS disjE));
|
|
|
16 |
(*
|
|
|
17 |
goal Option.thy "opt=None | (? x.opt=Some(x))";
|
|
|
18 |
by (option.induct_tac "opt" 1);
|
|
|
19 |
by (Simp_tac 1);
|
|
|
20 |
by (rtac disjI2 1);
|
|
|
21 |
by (rtac exI 1);
|
|
|
22 |
by (Asm_full_simp_tac 1);
|
|
|
23 |
qed"option_cases";
|
|
|
24 |
*)
|
|
|
25 |
goal Option.thy "P(case opt of None => a | Some(x) => b(x)) = \
|
|
|
26 |
\ ((opt = None --> P a) & (!x. opt = Some x --> P(b(x))))";
|
|
|
27 |
by (option.induct_tac "opt" 1);
|
|
|
28 |
by (Simp_tac 1);
|
|
|
29 |
by (Asm_full_simp_tac 1);
|
|
2031
|
30 |
by (Fast_tac 1);
|
|
2019
|
31 |
qed"expand_option_case";
|