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Proof step 10 from proof not-prime (previous step)

m | n, 2 ≤ n, m * m ≤ n, ∀ 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

User applied rule apply induction

And obtained the following new goals

Proof step 11:
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

Rule argument

subst: [n0] → [m]

Additional information

Used simplifier rules: divi-ls: ⊦ m < n0 → (n0 | m ↔ m = 0);%divi-zero-01: ⊦ 0 | m ↔ m = 0;% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≠ 1 → (m < 2 ↔ m = 0); (s)% ⊦ m ≠ n → (m < n ↔ ¬ n < m); (ss) Used terms: m