Theory: zip

Parents


Type constants


Term constants


Axioms


Definitions

ZIP
|- !y z x. ZIP (y,z) x = (y x,z x)
Zip_DEF
|- !a b. a Zip b = ZIP (a,b)
UNZIP
|- !y. UNZIP y = ((\x. FST (y x)),(\x. SND (y x)))

Theorems

PAIR_FORALL
|- !P. (!s. P s) = (!s1 s2. P (s1,s2))
PAIR_EXISTS
|- !P. (?s. P s) = (?s1 s2. P (s1,s2))
Zip
|- !a b x. (a Zip b) x = (a x,b x)
UNZIP_ZIP
|- !y. UNZIP (ZIP y) = y
ZIP_UNZIP
|- !y. ZIP (UNZIP y) = y
EXISTS_ZIP
|- !P. (?s. P s) = (?s1 s2. P (ZIP (s1,s2)))
EXISTS_Zip
|- !P. (?s. P s) = (?s1 s2. P (s1 Zip s2))
FORALL_ZIP
|- !P. (!s. P s) = (!s1 s2. P (ZIP (s1,s2)))
FORALL_Zip
|- !P. (!s. P s) = (!s1 s2. P (s1 Zip s2))