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Proof step 9 from proof divi-add (previous step)

⊦ (∃ n2. m * n2 = m * n1 + n0) ↔ (∃ n1. m * n1 = n0)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: coef-04: ⊦ m * n + m0 * n = m1 * n ↔ ¬ ¬(m + m0 = m1 ∨ n = 0); from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2