\x.x = I \x.y = Ky if x not in y \x.ab = S \x.a \x.b = \x.a (1) \x.b \x.a(n)b = \x.a (n+1) \x.b \x.(a =n= b) == \x.a =n+1= \x.b \x.(p =n> q) == (\x.p =n+1> \x.q) (a(n+1)b)x = (ax) (n) (bx) (a =n+1= b) x == (ax =n= bx) (p =n+1> q) x == (px =n> qx) Interpretation : a (0) b = ab a (1) b = the x for which ax = bx or for all x in U, ax = bx p =0> q : p => q p =1> q : p included in q