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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
n % m1 = 0, prime(m1), n | m, n | m0, 2 ≤ m1, m1 * m1 ≤ n ⊦ m + m0 = 1, m1 = 0, n = 1, n = 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% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)