At: quotient of nsubn 2 1 2 1 1 2 1 1 2 1 1 2 2 3 1 2
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). k E (n-1))
19. n-1 i,j:n//(i E j)
20. f1: (m+1)(i,j:n//(i E j))
21. f1 = (
x.if x=
m
n-1 else f(x) fi)
22. x: i,j:n//(i E j)
23. (x Eb (n-1))
g(x) (m+1)
By:
RWO "17" 23
THEN
FwdThru
Thm* n:{1...}, E:(nnProp).
(EquivRel i,j:n. i E j)
(x:i,j:n//(i E j). x = n-1 i,j:n//(i E j) x i,j:(n-1)//(i E j))
[23]
Generated subgoals:None
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