Step
*
of Lemma
nim-sum-assoc
∀[x,y,z:ℕ]. (nim-sum(x;nim-sum(y;z)) = nim-sum(nim-sum(x;y);z) ∈ ℤ)
BY
{ ((CompleteInductionOnNat THEN Auto) THEN CaseNat 0 `x' THEN Reduce 0 THEN Auto) }
1
1. x : ℕ
2. ∀x:ℕx. ∀[y,z:ℕ]. (nim-sum(x;nim-sum(y;z)) = nim-sum(nim-sum(x;y);z) ∈ ℤ)
3. y : ℕ
4. z : ℕ
5. ¬(x = 0 ∈ ℤ)
⊢ nim-sum(x;nim-sum(y;z)) = nim-sum(nim-sum(x;y);z) ∈ ℤ
Latex:
Latex:
\mforall{}[x,y,z:\mBbbN{}]. (nim-sum(x;nim-sum(y;z)) = nim-sum(nim-sum(x;y);z))
By
Latex:
((CompleteInductionOnNat THEN Auto) THEN CaseNat 0 `x' THEN Reduce 0 THEN Auto)
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