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At: fin dec fin 2 1 2 2 4 1 1 5
1. n:
2. 0 < n
3. T:Type, B:(TProp). (f:((n-1)T), g:(T(n-1)). InvFuns((n-1); T; f; g)) & (t:T. Dec(B(t))) (m:, f:(m{t:T| B(t) }), g:({t:T| B(t) }m). InvFuns(m; {t:T| B(t) }; f; g))
4. T: Type
5. B: TProp
6. f: nT
7. g: Tn
8. g o f = Id
9. f o g = Id
10. t:T. Dec(B(t))
11. f (n-1){t:T| g(t) < n-1 }
12. g {t:T| g(t) < n-1 }(n-1)
13. m:
14. f1: m{t:{t:T| g(t) < n-1 }| B(t) }
15. g@0: {t:{t:T| g(t) < n-1 }| B(t) }m
16. InvFuns(m; {t:{t:T| g(t) < n-1 }| B(t) }; f1; g@0)
17. B(f(n-1))
18. f2: (m+1){t:T| B(t) }
19. f2 = (x.if x=m f(n-1) else f1(x) fi)
20. g2: {t:T| B(t) }(m+1)
21. g2 = (x.if g(x)=n-1 m else g@0(x) fi)

m:, f:(m{t:T| B(t) }), g:({t:T| B(t) }m). InvFuns(m; {t:T| B(t) }; f; g)
By: InstConcl [m+1;f2;g2]
Generated subgoal:

1 InvFuns((m+1); {t:T| B(t) }; f2; g2)

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