Nuprl - Pf fin_dec_fin 2 1 2 2 4 1 1 3 1 1

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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. x: {t:T| B(t) }
21. g(x) = n-1

x {t:{t:T| g(t) < n-1 }| B(t) }

By: Analyze 20 THEN Analyze THEN Analyze

Generated subgoal:

1 20. x: T
21. B(x)
22. g(x) = n-1
g(x) < n-1

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