Theory: combin

Parents


Type constants


Term constants


Axioms


Definitions

o_DEF
|- !f g. f o g = (\x. f (g x))
K_DEF
|- K = (\x y. x)
S_DEF
|- S = (\f g x. f x (g x))
I_DEF
|- I = S K K

Theorems

o_THM
|- !f g x. (f o g) x = f (g x)
o_ASSOC
|- !f g h. f o g o h = (f o g) o h
K_THM
|- !x y. K x y = x
S_THM
|- !f g x. S f g x = f x (g x)
I_THM
|- !x. I x = x
I_o_ID
|- !f. (I o f = f) /\ (f o I = f)