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Proof step 11 from proof modprime (previous step)

m | n, ∀ m. 2 ≤ m ∧ m < n → n % m ≠ 0 ⊦ m = 1, m = n, n = 1, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
m ≠ 0 ⊦ m | n ↔ n % m = 0
Proof step 13:
n % m = 0, ∀ m. 2 ≤ m ∧ m < n → n % m ≠ 0 ⊦ m = n, m = 1, m = 0, n = 0, n = 1

Rule argument

spec: <toplevel> name: divi-mod seq: m ≠ 0 ⊦ m | n ↔ n % m = 0 subst: [n, m] → [n, m] flags: <all paths>

Additional information

Used simplifier rules: divi-zero-01: ⊦ 0 | m ↔ m = 0; Used terms: n, m