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Proof step 9 from proof square-even (previous step)

m = 2 * n1 + 1, m * m + m = 2 * n + 1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
2 * n = n1 * 6 + n1 * 4 * n1 + 1 ⊦

Rule argument

Additional information

Used simplifier rules: rsucc-01: ⊦ (m + 1) * n = m * n + n;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%dist: ⊦ m0 * (m + n) = m0 * m + m0 * n;%rdist: ⊦ m0 * (* m) + m0 * (* n) = m0 * (m + n);%add-num-01: n < n0 ⊦ m + (* n) = m0 + (* n0) ↔ m = m0 + (n0 - n); from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2