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Proof step 17 from proof gcdnex-prime (previous step)

prime(m1), n0 * m1 | m0, n0 * m1 | m, 2 ≤ n0, m1 ≤ n0, 2 ≤ m1 ⊦ n0 * m1 = 1, m + m0 = 1, m1 = 0, n0 = 0, ∃ n. prime(n) ∧ n ≠ 0 ∧ n ≠ 1 ∧ n | m ∧ n | m0

User applied rule exists right

And obtained the following new goals

Proof step 18:
prime(m1), n0 * m1 | m, n0 * m1 | m0, 2 ≤ m1, m1 ≤ n0, 2 ≤ n0 ⊦ n0 * m1 = 1, m + m0 = 1, m1 = 0, n0 = 0, prime(m1) ∧ m1 ≠ 0 ∧ m1 ≠ 1 ∧ m1 | m ∧ m1 | m0

Rule argument

pos: right 5 terms: m1 abort: F discard: T computed: T

Additional information

Used terms: m1