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Proof step 27 from proof max_prime_divisor-nls-02 (previous step)

i0 < 2, j < j * i0, prime(j), 2 ≤ j * i0, j < max_prime_divisor(i0), i0 < j * i0, 0 ≤ 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 inst: name: ls-same-01 seq: ⊦ 0 < i → (i < i * j ↔ 1 < j) subst: [j, i] → [j, i0] flags: rewrite

Additional information

Used simplifier rules: prime-not-neg: ⊦ j < 0 → ¬ prime(j);%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%irref: ⊦ ¬ i < i; from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%numlsledel: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); from specification int-abs%zero-ge-03: ⊦ i ≤ 0 → (0 ≤ i * j ↔ ¬ ¬(i = 0 ∨ j ≤ 0)); from specification int-mult%zero-gr-03: ⊦ i ≤ 0 → (0 < i * j ↔ ¬ ¬(j < 0 ∧ i ≠ 0)); from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls-same-03: ⊦ i < 0 → (i < i * j ↔ j < 1); from specification int-mult%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i0