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At: quotient of finite 1 1 1
1. n: {1...}
2. A: Type
3. R: AAProp
4. n ~ A
5. EquivRel x,y:A. x R y
6. x,y:A. Dec(x R y)
7. f: nA
8. Bij(n; A; f)
9. F:((x,y:n//(x R_f y))(x,y:A//(x R y))). Bij(x,y:n//(x R_f y); x,y:A//(x R y); F)

m:(n+1). m ~ (x,y:A//(x R y))
By: Inst Thm* f:(AB), R:(BBProp). (EquivRel x,y:B. x R y) (EquivRel x,y:A. x R_f y) [n;A;f;R]
Generated subgoal:

110. EquivRel x,y:n. x R_f y
m:(n+1). m ~ (x,y:A//(x R y))

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existsnatural_numberaddquotientuniversefunctionpropall