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Proof step 20 from proof not-prime (previous step)

m0 | n0, prime(m0), m0 * m0 ≤ n0, n0 < m, 2 < m * m, 2 ≤ m * n0, m0 * m0 < m, ∀ n1. n1 < m * n0 → ¬ prime(n1) ∧ 2 ≤ n1 → (∃ m. m | n1 ∧ prime(m) ∧ m * m ≤ n1) ⊦ n0 = 0, m = 1, n0 = 1, m * n0 = 1, m = 0, prime(n0), ∃ m0. m0 | m * n0 ∧ prime(m0) ∧ m0 * m0 ≤ m * n0

User applied rule exists right

And closed the goal!

Rule argument

pos: right 7 terms: m0 abort: F discard: F computed: F

Additional information

Used simplifier rules: divi-mult-01: ⊦ m | n → m | n * n0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%ls-10: ⊦ m ≤ n ∧ n0 ≠ 0 → ¬ n * n0 < m; from specification nat-mult Used terms: m0