Nuprl - Pf auto2_lemma_4 1 1 1 1 1 1 1 1 1 1 1 2

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At: auto2 lemma 4 1 1 1 1 1 1 1 1 1 1 1 2

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. a,b,c:Alph*. ||a||nn (a':Alph*. ||a'|| < ||a|| & R((a @ b),a' @ b) & R((a @ c),a' @ c))
12. ||l|| < nn

R((l @ b),l @ b) & R((l @ c),l @ c)

By: Analyze 4

Generated subgoal:

1 4. x:Alph*. R(x,x)
5. (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)))
6. b: Alph*
7. c: Alph*
8. n@0:
9. l:Alph*. ||l|| < n@0 (a':Alph*. ||a'|| < nn & R((l @ b),a' @ b) & R((l @ c),a' @ c))
10. l: Alph*
11. ||l|| = n@0
12. a,b,c:Alph*. ||a||nn (a':Alph*. ||a'|| < ||a|| & R((a @ b),a' @ b) & R((a @ c),a' @ c))
13. ||l|| < nn
R((l @ b),l @ b) & R((l @ c),l @ c)

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