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Proof step 7 from proof prime-prime (previous step)

∀ m. 2 ≤ m ∧ prime(m) ∧ m * m ≤ n → n % m ≠ 0 ⊦ n = 0, n = 1, prime(n)

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
¬ prime(n), 2 ≤ n ⊦ ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n
Proof step 9:
∀ m. 2 ≤ m ∧ prime(m) ∧ m * m ≤ n → n % m ≠ 0, ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n ⊦ n = 1, n = 0, prime(n)

Rule argument

spec: <toplevel> name: not-prime seq: ¬ prime(n), 2 ≤ n ⊦ ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n subst: [n] → [n]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≠ 1 → (n < 2 ↔ n = 0); (s) Used terms: n