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At: auto2 lemma 3 1 1 1 2
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. Bij(nn; (nn); f1)
18. i,j:(nn+1). i < j & (j.f1( < f((a[||a||-j..||a||]) @ b),f((a[||a||-j..||a||]) @ c) > ))(i) = (j.f1( < f((a[||a||-j..||a||]) @ b),f((a[||a||-j..||a||]) @ c) > ))(j) (nn)

a':Alph*. ||a'|| < ||a|| & R((a @ b),a' @ b) & R((a @ c),a' @ c)
By:
Analyze 18
THEN
Analyze 19
THEN
Analyze 20
THEN
Reduce 21
Generated subgoal:

118. 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) > )
a':Alph*. ||a'|| < ||a|| & R((a @ b),a' @ b) & R((a @ c),a' @ c)

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