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

PrintForm Definitions finite sets Sections AutomataTheory Doc

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)

f o g = Id

By: Ext

Generated subgoals:

1 13. x: {t:T| g(t) < n-1 }
(f o g)(x) = Id(x)

2 {t:T| g(t) < n-1 } = {t:T| g(t) < n-1 }

3 f o g = f o g

4 Id = Id

About:

1	13. `x:` `{t:T\| g(t) < n-1 }` `(f o g)(x) = Id(x)`
2	`{t:T\| g(t) < n-1 } = {t:T\| g(t) < n-1 }`
3	`f o g = f o g`
4	`Id = Id`