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

(l:Alph*. ||l|| < n@0 (a.a':Alph*. ||a'|| < nn & R((a @ b),a' @ b) & R((a @ c),a' @ c))(l)) (l:Alph*. ||l|| = n@0 (a.a':Alph*. ||a'|| < nn & R((a @ b),a' @ b) & R((a @ c),a' @ c))(l))
By:
Reduce 0
THEN
UnivCD
Generated subgoal:

18. 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
a':Alph*. ||a'|| < nn & R((l @ b),a' @ b) & R((l @ c),a' @ c)

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impliesalllistless_thanapplylambdaexistsand
multiplyequalintuniversefunctionpropnatural_number