Nuprl - Pf inv_of_fin_is_fin 1 1 2 2 1 2 1 1 1 1

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At: inv of fin is fin 1 1 2 2 1 2 1 1 1 1

1. T: Type
2. S: Type
3. f: TS
4. Fin(S)
5. s:S. Dec(t:T. f(t) = s)
6. EquivRel x,y:T. f(x) = f(y)
7. f@0: {s:S| t:T. f(t) = s }T
8. s:{s:S| t:T. f(t) = s }. f(f@0(s)) = s

f@0 = f@0 {s:S| t:T. f(t) = s }(x,y:T//(f(x) = f(y)))

By: Ext

Generated subgoals:

1 f@0 = f@0 {s:S| t:T. f(t) = s }(x,y:T//(f(x) = f(y)))

2 9. x: {s:S| t:T. f(t) = s }
f@0(x) = f@0(x) x,y:T//(f(x) = f(y))

3 {s:S| t:T. f(t) = s } = {s:S| t:T. f(t) = s }

About:

1	`f@0 = f@0 {s:S\| t:T. f(t) = s }(x,y:T//(f(x) = f(y)))`
2	9. `x:` `{s:S\| t:T. f(t) = s }` `f@0(x) = f@0(x) x,y:T//(f(x) = f(y))`
3	`{s:S\| t:T. f(t) = s } = {s:S\| t:T. f(t) = s }`