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At: auto2 lemma 7 1 1 2 1
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))

Dec(k:(nn), l:{l:(Alph*)| ||l|| = k }. L(l @ x) = L(l @ y))
By: Inst Thm* R:(TProp). Fin(T) & (t:T. Dec(R(t))) Dec(t:T. R(t)) [(nn);k.l:{l:(Alph*)| ||l|| = k }. L(l @ x) = L(l @ y)]
Generated subgoals:

115. (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))
Fin((nn))
215. (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)
Dec((k.l:{l:(Alph*)| ||l|| = k }. L(l @ x) = L(l @ y) )(t))
316. Dec(t:(nn). (k.l:{l:(Alph*)| ||l|| = k }. L(l @ x) = L(l @ y) )(t))
Dec(k:(nn), l:{l:(Alph*)| ||l|| = k }. L(l @ x) = L(l @ y))

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