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Proof step 19 from proof not-prime (previous step)

∃ m. m | n0 ∧ prime(m) ∧ m * m ≤ n0, n0 < m, 2 < m * m, 2 ≤ m * n0, ∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
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

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat