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At: auto2 lemma 8 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*

Dec(x@0:Alph*. L(x@0 @ x) = L(x@0 @ y))
By: Inst Thm* R:(Alph*Alph*Prop), n:, L:(Alph*), m:. (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))) & (v:(mAlph*). l:Alph*. L(l) (i:m. R(l,v(i)))) & Fin(Alph) (x,y:Alph*. Dec(l:Alph*. L(l @ x) = L(l @ y))) [Alph;R;n;L;m]
Generated subgoals:

1 (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))) & (v:(mAlph*). l:Alph*. L(l) (i:m. R(l,v(i)))) & Fin(Alph)
215. x,y:Alph*. Dec(l:Alph*. L(l @ x) = L(l @ y))
Dec(x@0:Alph*. L(x@0 @ x) = L(x@0 @ y))

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