Nuprl - Pf fin_dec_fin 2 1 2 2 3 1

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:((n-1){t:T| g(t) < n-1 }), g@0:({t:T| g(t) < n-1 }(n-1)). InvFuns((n-1); {t:T| g(t) < n-1 }; f; g@0)

By: InstConcl [f;g]

Generated subgoals:

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

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

3 InvFuns((n-1); {t:T| g(t) < n-1 }; f; g)

4 13. g@0: {t:T| g(t) < n-1 }(n-1)
InvFuns((n-1); {t:T| g(t) < n-1 }; f; g@0) Prop

5 13. f1: (n-1){t:T| g(t) < n-1 }
(g@0:({t:T| g(t) < n-1 }(n-1)). InvFuns((n-1); {t:T| g(t) < n-1 }; f1; g@0)) Prop

About:

1	`f (n-1){t:T\| g(t) < n-1 }`
2	`g {t:T\| g(t) < n-1 }(n-1)`
3	`InvFuns((n-1); {t:T\| g(t) < n-1 }; f; g)`
4	13. `g@0:` `{t:T\| g(t) < n-1 }(n-1)` `InvFuns((n-1); {t:T\| g(t) < n-1 }; f; g@0) Prop`
5	13. `f1:` `(n-1){t:T\| g(t) < n-1 }` `(g@0:({t:T\| g(t) < n-1 }(n-1)). InvFuns((n-1); {t:T\| g(t) < n-1 }; f1; g@0)) Prop`