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1. Alph: Type
2. R: Alph*Alph*Prop
3. n:
4. x:Alph*. R(x,x)
5. x,y:Alph*. R(x,y) R(y,x)
6. x,y,z:Alph*. R(x,y) & R(y,z) R(x,z)
7. x,y,z:Alph*. R(x,y) R((z @ x),z @ y)
8. w: nAlph*
9. l:Alph*. i:n. R(l,w(i))
10. a: Alph*
11. b: Alph*
12. c: Alph*
13. ||a||nn
14. f: Alph*n
15. x:Alph*. R(x,w(f(x)))
16. f1: nn(nn)
17. Inj(nn; (nn); f1) & Surj(nn; (nn); f1)
18. i: (nn+1)
19. j: (nn+1)
20. i < j
21. f1( < f((a[||a||-i..||a||]) @ b),f((a[||a||-i..||a||]) @ c) > ) = f1( < f((a[||a||-j..||a||]) @ b),f((a[||a||-j..||a||]) @ c) > )

R((a @ b),((a[0..||a||-j]) @ (a[||a||-i..||a||])) @ b) & R((a @ c),((a[0..||a||-j]) @ (a[||a||-i..||a||])) @ c)
By:
Analyze 17
THEN
Unfold `inject` 17
Generated subgoal:

117. a1,a2:(nn). f1(a1) = f1(a2) a1 = a2
18. Surj(nn; (nn); f1)
19. i: (nn+1)
20. j: (nn+1)
21. i < j
22. f1( < f((a[||a||-i..||a||]) @ b),f((a[||a||-i..||a||]) @ c) > ) = f1( < f((a[||a||-j..||a||]) @ b),f((a[||a||-j..||a||]) @ c) > )
R((a @ b),((a[0..||a||-j]) @ (a[||a||-i..||a||])) @ b) & R((a @ c),((a[0..||a||-j]) @ (a[||a||-i..||a||])) @ c)

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