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Proof step 2 from proof dist (previous step)

∀ m, n. m1 * (m + n) = m1 * m + m1 * n ⊦ m1 +1 * (m + n) = m1 +1 * m + m1 +1 * n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ m, n. m1 * (m + n) = m1 * m + m1 * n ⊦ m1 * (m + n) = m1 * m + m1 * n

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;%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%succ: ⊦ m +1 = m + 1; from specification nat-basic2