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Proof step 13 from proof gcdnex-prime (previous step)

n | m, n | m0 ⊦ n = 1, n = 0, m = 1, m0 = 1, 1 < n ∧ (∀ m. 2 ≤ m ∧ prime(m) ∧ m * m ≤ n → n % m ≠ 0), ∃ n. prime(n) ∧ n ≠ 0 ∧ n ≠ 1 ∧ n | m ∧ n | m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
n % m1 = 0, n | m, n | m0, 2 ≤ m1, prime(m1), m1 * m1 ≤ n ⊦ n = 1, n = 0, m = 1, m0 = 1, m1 = 0, ∃ n. prime(n) ∧ n ≠ 0 ∧ n ≠ 1 ∧ n | m ∧ n | m0

Rule argument

Additional information

Used simplifier rules: not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%one: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); from specification nat-basic1