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Proof step 1 from proof mod-succ-02 (conclusion)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
n ≠ 0 ⊦ m % n + 1 ≠ n → (m + 1) % n = m % n + 1
Proof step 3:
m % n + 1 ≠ n → (m + 1) % n = m % n + 1, n ≠ 0 ⊦ (m + 1) % n = 0 → m % n = n - 1

Rule argument

spec: nat-div inst: name: mod-succ-01 seq: n ≠ 0 ⊦ m % n + 1 ≠ n → (m + 1) % n = m % n + 1 subst: [n, m] → [n, m] flags: current, []

Additional information

Used terms: n, m