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Proof step 12 from proof not-prime (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
2 < m * m, n < m * m, m | n, 2 ≤ n, ∀ n0. n0 < n → ¬ prime(n0) ∧ 2 ≤ n0 → (∃ m. m | n0 ∧ prime(m) ∧ m * m ≤ n0) ⊦ n = 1, m = n, m = 1, n = 0, m = 0, ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%sqzero: ⊦ m * m = 0 ↔ m = 0; from specification nat-mult%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat