Theory: pair_thms

Parents


Type constants


Term constants


Axioms


Definitions


Theorems

CURRY_UNCURRY_THM
|- !f. CURRY (UNCURRY f) = f
UNCURRY_CURRY_THM
|- !f. UNCURRY (CURRY f) = f
CURRY_ONE_ONE_THM
|- (CURRY f = CURRY g) = f = g
UNCURRY_ONE_ONE_THM
|- (UNCURRY f = UNCURRY g) = f = g
PFORALL_THM
|- !f. (!x y. f x y) = (!(x,y). f x y)
PEXISTS_THM
|- !f. (?x y. f x y) = (?(x,y). f x y)
NOT_FORALL_THM
|- !f. ~(!x. f x) = (?x. ~(f x))
NOT_EXISTS_THM
|- !f. ~(?x. f x) = (!x. ~(f x))
FORALL_AND_THM
|- !f g. (!x. f x /\ g x) = (!x. f x) /\ (!x. g x)
EXISTS_OR_THM
|- !f g. (?x. f x \/ g x) = (?x. f x) \/ (?x. g x)
LEFT_AND_FORALL_THM
|- !Q f. (!x. f x) /\ Q = (!x. f x /\ Q)
RIGHT_AND_FORALL_THM
|- !P g. P /\ (!x. g x) = (!x. P /\ g x)
LEFT_OR_EXISTS_THM
|- !Q f. (?x. f x) \/ Q = (?x. f x \/ Q)
RIGHT_OR_EXISTS_THM
|- !P g. P \/ (?x. g x) = (?x. P \/ g x)
BOTH_EXISTS_AND_THM
|- !P Q. (?x. P /\ Q) = (?x. P) /\ (?x. Q)
LEFT_EXISTS_AND_THM
|- !Q f. (?x. f x /\ Q) = (?x. f x) /\ Q
RIGHT_EXISTS_AND_THM
|- !P g. (?x. P /\ g x) = P /\ (?x. g x)
BOTH_FORALL_OR_THM
|- !P Q. (!x. P \/ Q) = (!x. P) \/ (!x. Q)
LEFT_FORALL_OR_THM
|- !Q f. (!x. f x \/ Q) = (!x. f x) \/ Q
RIGHT_FORALL_OR_THM
|- !P g. (!x. P \/ g x) = P \/ (!x. g x)
BOTH_FORALL_IMP_THM
|- !P Q. (!x. P ==> Q) = (?x. P) ==> (!x. Q)
LEFT_FORALL_IMP_THM
|- !Q f. (!x. f x ==> Q) = (?x. f x) ==> Q
RIGHT_FORALL_IMP_THM
|- !P g. (!x. P ==> g x) = P ==> (!x. g x)
BOTH_EXISTS_IMP_THM
|- !P Q. (?x. P ==> Q) = (!x. P) ==> (?x. Q)
LEFT_EXISTS_IMP_THM
|- !Q f. (?x. f x ==> Q) = (!x. f x) ==> Q
RIGHT_EXISTS_IMP_THM
|- !P g. (?x. P ==> g x) = P ==> (?x. g x)