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1. Alph: Type
2. R: Alph*Alph*Prop
3. n:
4. L: Alph*
5. m:
6. x:Alph*. R(x,x)
7. x,y:Alph*. R(x,y) R(y,x)
8. x,y,z:Alph*. R(x,y) & R(y,z) R(x,z)
9. x,y,z:Alph*. R(x,y) R((z @ x),z @ y)
10. w:(nAlph*). l:Alph*. i:n. R(l,w(i))
11. v:(mAlph*). l:Alph*. L(l) (i:m. R(l,v(i)))
12. Fin(Alph)
13. x: Alph*
14. y: Alph*
15. (l:Alph*. L(l @ x) = L(l @ y)) (k:(nn), l:{l:(Alph*)| ||l|| = k }. L(l @ x) = L(l @ y))
16. (l:Alph*. L(l @ x) = L(l @ y)) (k:(nn), l:{l:(Alph*)| ||l|| = k }. L(l @ x) = L(l @ y))
17. t: (nn)
18. Fin({l:(Alph*)| ||l|| = t })
19. l:Alph*. ||l|| = t ||l|| = t

Fin({l:(Alph*)| ||l|| = t })
By: Inst Thm* (T ~ U) & Fin(T) Fin(U) [{l:(Alph*)| ||l|| = t };{l:(Alph*)| ||l|| = t }]
Generated subgoals:

1 {l:(Alph*)| ||l|| = t } ~ {l:(Alph*)| ||l|| = t }
220. Fin({l:(Alph*)| ||l|| = t })
Fin({l:(Alph*)| ||l|| = t })

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