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Proof step 4 from proof mod-succ-02 (previous step)

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

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;;% ⊦ m +1 = m + 1; (s)% ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)