At: fin dec fin 2 1 2 2 4 1 1 5 1 2 1 2 2 2 1
1. n: 
2. 0 < n
3. 
T:Type, B:(T
Prop).
(
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. g@0 o f1 = Id
17. f1 o g@0 = Id
18. B(f(n-1))
19. f2: (m+1){t:T| B(t) }
20. f2 = (
x.if x=
m
f(n-1) else f1(x) fi)
21. g2: {t:T| B(t) }(m+1)
22. g2 = (x.if g(x)=n-1 m else g@0(x) fi)
23. x: {t:T| B(t) }
24. 
g(x) = n-1
25. x {t:{t:T| g(t) < n-1 }| B(t) }
26. g@0(x) = m
(f1 o g@0)(x) = x
By:
HypSubst 17 0
THEN
Reduce 0
Generated subgoals:None
About:
