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Proof step 11 from proof not-prime (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
prime(m0), m | n, m0 | m, m0 | n, 2 ≤ n, m * m ≤ n, m0 * m0 ≤ m, ∀ n0. n0 < n → 2 ≤ n0 → prime(n0) ∨ (∃ m. m | n0 ∧ prime(m) ∧ m * m ≤ n0) ⊦ m = n, m = 1, n = 0, n = 1, prime(m), ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n

Rule argument

Additional information

Used simplifier rules: divi-trans: ⊦ n0 | m ∧ m | n → n0 | n;%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat