JavaScript Y combinator and Z combinator

Note that this topic is a sub-set of lambda calculus. First how to prove that Y combinator is a fixed-point combinator: Y f = (lg. (lx. g (x x)) (lx. g (x x))) f = (lx. f (x x)) (lx. f (x x)) = l(lx. f (x x)). f (x x) = f ((lx. f (x x)) (...