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1. Alph: Type
2. R: Alph*Alph*Prop
3. n:
4. (x:Alph*. R(x,x)) & (x,y:Alph*. R(x,y) R(y,x)) & (x,y,z:Alph*. R(x,y) & R(y,z) R(x,z)) & (x,y,z:Alph*. R(x,y) R((z @ x),z @ y)) & (w:(nAlph*). l:Alph*. i:n. R(l,w(i)))
5. b: Alph*
6. c: Alph*
7. n@0:
8. l:Alph*. ||l|| < n@0 (a':Alph*. ||a'|| < nn & R((l @ b),a' @ b) & R((l @ c),a' @ c))
9. l: Alph*
10. ||l|| = n@0
11. ||l|| < nn
12. a': Alph*
13. ||a'|| < ||l|| & R((l @ b),a' @ b) & R((l @ c),a' @ c)

a':Alph*. ||a'|| < nn & R((l @ b),a' @ b) & R((l @ c),a' @ c)
By: Witness8 a'
Generated subgoal:

18. l: Alph*
9. ||l|| = n@0
10. ||l|| < nn
11. a': Alph*
12. ||a'|| < ||l|| & R((l @ b),a' @ b) & R((l @ c),a' @ c)
13. ||a'|| < n@0 (a'@0:Alph*. ||a'@0|| < nn & R((a' @ b),a'@0 @ b) & R((a' @ c),a'@0 @ c))
a':Alph*. ||a'|| < nn & R((l @ b),a' @ b) & R((l @ c),a' @ c)

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