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At: fin dec fin 2 1 2 2 3 1 3 2 1 2
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. x: {t:T| g(t) < n-1 }
14. (f o g)(x) = x

(f o g)(x) = Id(x)
By:
Reduce -1
THEN
Reduce 0
Generated subgoal:

114. f(g(x)) = x
f(g(x)) = x

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equalsetless_thanapplysubtractnatural_numberintall
universefunctionpropimpliesandexistsmember