At: one2one preserves fin111111111111111111 1. T: Type 2. U: Type 3. f: TU 4. g: UT 5. g o f = Id 6. f o g = Id 7. n: 8. f1: nT 9. Inj(n; T; f1) 10. Surj(n; T; f1) 11. a1: n 12. a2: n 13. (f o f1)(a1) = (f o f1)(a2) 14. (g o f o f1)(a1) = (g o f o f1)(a2)
a1 = a2 By: RWH
(LemmaC
Thm*f:(AB), g:(BC), h:(CD). h o (g o f) = (h o g) o f AD)
14 Generated subgoal: