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At: fun preserves fin 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1. S: Type
2. T: Type
3. n:
4. f: nS
5. g: Sn
6. g o f = Id & f o g = Id
7. n1:
8. f1: n1T
9. g1: Tn1
10. g1 o f1 = Id
11. f1 o g1 = Id
12. f2: (nn1)(n1n)
13. g2: (n1n)nn1
14. g2 o f2 = Id
15. f2 o g2 = Id

f:((n1n)ST), g:((ST)(n1n)). g o f = Id (n1n)(n1n) & f o g = Id (ST)ST
By: Witness h.f1 o g2(h) o g
Generated subgoal:

1 g@0:((ST)(n1n)). g@0 o (h.f1 o g2(h) o g) = Id & (h.f1 o g2(h) o g) o g@0 = Id

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existsfunctionnatural_numberandequallambdaapplyuniverse