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Proof step 28 from proof max_prime_divisor-nls-02 (previous step)

j < j * i0, i0 < 2, j < max_prime_divisor(i0), 0 < j * i0, i0 < j * i0, prime(j), 2 ≤ j * i0, 0 ≤ j * i0, ∀ j0. j < j0 ∧ j0 < j * i0 ∧ prime(j0) → ¬ j0 | j * i0 ⊦ prime(j * i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: ls-same-01 seq: ⊦ 0 < i → (i < i * j ↔ 1 < j) subst: [j, i] → [j, i0] flags: <all paths>

Additional information

Used simplifier rules: prime-not-neg: ⊦ j < 0 → ¬ prime(j);% ⊦ 0 < j → (j < 2 ↔ j = 1); (s)% ⊦ i = 1 → i * j = j; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ ¬ i < i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); (s)% ⊦ i ≤ 0 → (0 < i * j ↔ j < 0 ∧ i ≠ 0); (s)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < 0 → (0 ≤ i * j ↔ j ≤ 0); (s)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i0