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Proof step 3 from proof mod-succ-02 (previous step)

m % n + 1 ≠ n → (m + 1) % n = m % n + 1, n ≠ 0 ⊦ (m + 1) % n = 0 → m % n = n - 1

User applied rule structural induction

And closed the goal!

Rule argument

indvar: n

Additional information

Used simplifier rules: mod-succ-01: n ≠ 0 ⊦ m % n + 1 ≠ n → (m + 1) % n = m % n + 1;%nat freely generated by 0, +1;;%succ: ⊦ m +1 = m + 1; from specification nat-basic2%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2