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Proof step 1 from proof mod-neq-03 (conclusion)

⊦ n1 < n0 ∧ n0 < n ∧ n1 ≠ 0 → m0 * n + n0 + 1 ≠ m * n + n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m0 * n + n0 + 1 = m * n + n1, n1 < n, n0 < n, n1 < n0, n1 + 1 < n ⊦ n = 0, n0 = 0, n1 = 0

Rule argument

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2%trans-1: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic1%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1