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At: surj is inj gen 1 1 1 1 2 1 1 1 1 2 1 1
1. A: Type
2. B: Type
3. f: AB
4. f1: AB
5. g: BA
6. InvFuns(A; B; f1; g)
7. n:
8. f2: nB
9. g1: Bn
10. g1 o f2 = Id
11. f2 o g1 = Id
12. Surj(A; B; f)
13. a1: A
14. a2: A
15. f(a1) = f(a2)
16. g1(f1(a1)) = g1(f1(a2))
17. (f2 o g1)(f1(a1)) = (f2 o g1)(f1(a2))

a1 = a2
By:
RWH (HypC 11) 17
THEN
Reduce 17
Generated subgoal:

117. f1(a1) = f1(a2)
a1 = a2

About:
equaluniversefunctionnatural_numberapply