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Proof step 2 from proof not-prime (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
2 ≤ n, ∀ n0. n0 < n → ¬ prime(n0) ∧ 2 ≤ n0 → (∃ m. m | n0 ∧ prime(m) ∧ m * m ≤ n0) ⊦ n = 0, prime(n), ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n

Rule argument

Additional information

Used simplifier rules: not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat