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Proof step 2 from proof mod-neq-03 (previous step)

m0 * n + n0 + 1 = m * n + n1, n1 < n0, n0 < n ⊦ n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m0 * n + n0 + 1 = m * n + n1, n1 < n, n1 < n0, n0 < n, n1 + 1 < n ⊦ n1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%trans-01: ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic