Nuprl - Pf quotient_of_nsubn 2 1 2 1 1 2 1 1 2 1 1 1 1 4

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At: quotient of nsubn 2 1 2 1 1 2 1 1 2 1 1 1 1 4

1. n: {1+1...}
2. E:((n-1)(n-1)Prop). (EquivRel x,y:(n-1). x E y) & (x,y:(n-1). Dec(x E y)) (m:(n-1+1). m ~ (i,j:(n-1)//(i E j)))
3. E: nnProp
4. EquivRel x,y:n. x E y
5. x,y:n. Dec(x E y)
6. EquivRel x,y:(n-1). x E y
7. m: (n-1+1)
8. f: m(i,j:(n-1)//(i E j))
9. g: (i,j:(n-1)//(i E j))m
10. InvFuns(m; i,j:(n-1)//(i E j); f; g)
11. x:m. f(x) i,j:n//(i E j)
12. a:n. a E a
13. a,b:n. (a E b) (b E a)
14. a,b,c:n. (a E b) (b E c) (a E c)
15. x,y:i,j:n//(i E j). Dec(x = y)
16. Eb: (i,j:n//(i E j))(i,j:n//(i E j))
17. x,y:i,j:n//(i E j). (x Eb y) x = y
18. k: (n-1)
19. k E (n-1)

InvFuns(m; i,j:n//(i E j); x.f(x); x.if x Eb (n-1) g(k) else g(x) fi)

By: Analyze 0 THEN Eval [`compose`;`tidentity`;`identity`] 0

Generated subgoals:

1 (x.if (f(x)) Eb (n-1) g(k) else g(f(x)) fi) = (x.x) mm

2 (x.f(if x Eb (n-1) g(k) else g(x) fi)) = (x.x) (i,j:n//(i E j))(i,j:n//(i E j))

About:

1	`(x.if (f(x)) Eb (n-1) g(k) else g(f(x)) fi) = (x.x) mm`
2	`(x.f(if x Eb (n-1) g(k) else g(x) fi)) = (x.x) (i,j:n//(i E j))(i,j:n//(i E j))`