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Proof step 2 from proof mod-succ-02 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
n ≠ 0 ⊦ m % n + 1 ≠ n → (m + 1) % n = m % n + 1
Proof step 4:
(m + 1) % n = 0, m % n + 1 ≠ n → (m + 1) % n = m % n + 1 ⊦ m % n = n - 1, n = 0

Rule argument

spec: <toplevel> name: mod-succ-01 seq: n ≠ 0 ⊦ m % n + 1 ≠ n → (m + 1) % n = m % n + 1 subst: [n, m] → [n, m]

Additional information

Used terms: n, m