At: list quo choice pls11121 1. q: 2. E: q*q*Prop 3. EquivRel x,y:q*. x E y 4. x,y:q*. Dec(x E y) 5. f: q* 6. g: q* 7. g o f = Id 8. f o g = Id 9. h: 10. (n,k:. (n (x,y. (g(x)) E (g(y))) k) h(n) = h(k)) & (n:. n (x,y. (g(x)) E (g(y))) (h(n)))
(x,y:q*. (x E y) (g o h o f)(x) = (g o h o f)(y)) & (x:q*. x E ((g o h o f)(x))) By: Reduce 10 Generated subgoal:
10. (n,k:. ((g(n)) E (g(k))) h(n) = h(k)) & (n:. (g(n)) E (g(h(n)))) (x,y:q*. (x E y) (g o h o f)(x) = (g o h o f)(y)) & (x:q*. x E ((g o h o f)(x)))