(* Title: HOL/MiniML/Maybe.ML
ID: $Id$
Author: Wolfgang Naraschewski and Tobias Nipkow
Copyright 1996 TU Muenchen
*)
(* constructor laws for option_bind *)
Goalw [option_bind_def] "option_bind (Some s) f = (f s)";
by (Simp_tac 1);
qed "option_bind_Some";
Goalw [option_bind_def] "option_bind None f = None";
by (Simp_tac 1);
qed "option_bind_None";
Addsimps [option_bind_Some,option_bind_None];
(* expansion of option_bind *)
Goalw [option_bind_def] "P(option_bind res f) = \
\ ((res = None --> P None) & (!s. res = Some s --> P(f s)))";
by (rtac option.split 1);
qed "split_option_bind";
Goal
"((option_bind m f) = None) = ((m=None) | (? p. m = Some p & f p = None))";
by (simp_tac (simpset() addsplits [split_option_bind]) 1);
qed "option_bind_eq_None";
Addsimps [option_bind_eq_None];
(* auxiliary lemma *)
Goal "(y = Some x) = (Some x = y)";
by ( simp_tac (simpset() addsimps [eq_sym_conv]) 1);
qed "rotate_Some";