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

PrintForm Definitions finite sets Sections AutomataTheory Doc

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

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

By: Analyze 0 THEN Analyze 0

Generated subgoals:

1 9. a1: {s:S| t:T. f(t) = s }
a2:{s:S| t:T. f(t) = s }. f@0(a1) = f@0(a2) x,y:T//(f(x) = f(y)) a1 = a2

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

About:

1	9. `a1:` `{s:S\| t:T. f(t) = s }` `a2:{s:S\| t:T. f(t) = s }. f@0(a1) = f@0(a2) x,y:T//(f(x) = f(y)) a1 = a2`
2	9. `b:` `x,y:T//(f(x) = f(y))` `a:{s:S\| t:T. f(t) = s }. f@0(a) = b x,y:T//(f(x) = f(y))`