Added syntax for "asm_lr" simplifier option.
(* Title: FOL/ifol.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Intuitionistic first-order logic
*)
IFOL = Pure +
classes
term < logic
default
term
types
o
arities
o :: logic
consts
Trueprop :: "o => prop" ("(_)" 5)
True, False :: "o"
(* Connectives *)
"=" :: "['a, 'a] => o" (infixl 50)
"~=" :: "['a, 'a] => o" ("(_ ~=/ _)" [50, 51] 50)
Not :: "o => o" ("~ _" [40] 40)
"&" :: "[o, o] => o" (infixr 35)
"|" :: "[o, o] => o" (infixr 30)
"-->" :: "[o, o] => o" (infixr 25)
"<->" :: "[o, o] => o" (infixr 25)
(* Quantifiers *)
All :: "('a => o) => o" (binder "ALL " 10)
Ex :: "('a => o) => o" (binder "EX " 10)
Ex1 :: "('a => o) => o" (binder "EX! " 10)
translations
"x ~= y" == "~ (x = y)"
rules
(* Equality *)
refl "a=a"
subst "[| a=b; P(a) |] ==> P(b)"
(* Propositional logic *)
conjI "[| P; Q |] ==> P&Q"
conjunct1 "P&Q ==> P"
conjunct2 "P&Q ==> Q"
disjI1 "P ==> P|Q"
disjI2 "Q ==> P|Q"
disjE "[| P|Q; P ==> R; Q ==> R |] ==> R"
impI "(P ==> Q) ==> P-->Q"
mp "[| P-->Q; P |] ==> Q"
FalseE "False ==> P"
(* Definitions *)
True_def "True == False-->False"
not_def "~P == P-->False"
iff_def "P<->Q == (P-->Q) & (Q-->P)"
(* Unique existence *)
ex1_def "EX! x. P(x) == EX x. P(x) & (ALL y. P(y) --> y=x)"
(* Quantifiers *)
allI "(!!x. P(x)) ==> (ALL x.P(x))"
spec "(ALL x.P(x)) ==> P(x)"
exI "P(x) ==> (EX x.P(x))"
exE "[| EX x.P(x); !!x. P(x) ==> R |] ==> R"
(* Reflection *)
eq_reflection "(x=y) ==> (x==y)"
iff_reflection "(P<->Q) ==> (P==Q)"
end