Nuprl - Pf quotient_of_nsubn 2 1 2 1 1 2 1 1 2 1 1 2 2 3 3 1 1 1 4 2 1 1 1 1 1

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At: quotient of nsubn 2 1 2 1 1 2 1 1 2 1 1 2 2 3 3 1 1 1 4 2 1 1 1 1 1

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. n-1 i,j:n//(i E j)
19. f1: (m+1)(i,j:n//(i E j))
20. f1 = (x.if x=m n-1 else f(x) fi)
21. g1: (i,j:n//(i E j))(m+1)
22. g1 = (x.if x Eb (n-1) m else g(x) fi)
23. x: (m+1)
24. x = m
25. (f(x)) Eb (n-1)
26. f(x) = n-1 i,j:n//(i E j)
27. y1: (n-1)
28. y2: (n-1)
29. y1 E y2
30. y1 = f(x) i,j:n//(i E j)
31. x,y:i,j:(n-1)//(i E j). x = y i,j:n//(i E j) x = y i,j:(n-1)//(i E j)

y1 E (n-1)

By: Assert (y1 = n-1)

Generated subgoal:

1 32. y1 = n-1 i,j:n//(i E j)
y1 E (n-1)

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