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At: fun preserves fin 1 1 1 1 1 1 1 1 1 1 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
16. x: (n1n)

f2(Id o g2(x) o g o f) = x
By: Analyze 6
Generated subgoal:

16. g o f = Id
7. f o g = Id
8. n1:
9. f1: n1T
10. g1: Tn1
11. g1 o f1 = Id
12. f1 o g1 = Id
13. f2: (nn1)(n1n)
14. g2: (n1n)nn1
15. g2 o f2 = Id
16. f2 o g2 = Id
17. x: (n1n)
f2(Id o g2(x) o g o f) = x

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equalnatural_numberapplyuniversefunctionand