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At: surj is inj gen 1 1 1 1 2 1 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. InvFuns(n; B; f2; g1)
11. Surj(A; B; f)
12. a1,a2:n. (g1 o f o g o f2)(a1) = (g1 o f o g o f2)(a2) a1 = a2
13. a1: A
14. a2: A
15. f(a1) = f(a2)

a1 = a2
By:
Witness12 g1(f1(a1))
THEN
Witness15 g1(f1(a2))
Generated subgoal:

112. a1: A
13. a2: A
14. f(a1) = f(a2)
15. (g1 o f o g o f2)(g1(f1(a1))) = (g1 o f o g o f2)(g1(f1(a2))) g1(f1(a1)) = g1(f1(a2))
a1 = a2

About:
equalapplyuniversefunctionnatural_numberallimplies