PrintForm Definitions relation autom Sections AutomataTheory Doc

At: quotient 1 1 corr 1 1 1 5
1. A: Type
2. B: Type
3. f: AB
4. R: BBProp
5. Bij(A; B; f)
6. EquivRel x,y:B. x R y
7. EquivRel x,y:A. x R_f y
8. g: BA
9. InvFuns(A; B; f; g)
10. F: (x,y:A//(x R_f y))(x,y:B//(x R y))
11. F = (x.f(x))
12. G: (x,y:B//(x R y))(x,y:A//(x R_f y))
13. G = g (x,y:B//(x R y))(x,y:A//(x R_f y))

F:((x,y:A//(x R_f y))(x,y:B//(x R y))). Bij(x,y:A//(x R_f y); x,y:B//(x R y); F)
By: Inst Thm* f:(AB), g:(BA). InvFuns(A; B; f; g) Bij(A; B; f) [x,y:A//(x R_f y);x,y:B//(x R y);F;G]
Generated subgoals:

1 InvFuns(x,y:A//(x R_f y); x,y:B//(x R y); F; G)
214. Bij(x,y:A//(x R_f y); x,y:B//(x R y); F)
F:((x,y:A//(x R_f y))(x,y:B//(x R y))). Bij(x,y:A//(x R_f y); x,y:B//(x R y); F)

About:
existsfunctionquotientuniversepropequallambdaapply