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Proof step 97 from proof isSquare-mult-aux (previous step)

i0 * i0 = i * i * i2, max_prime_divisor(j0) * i0 = j0, 0 < j0, 0 < i, prime(max_prime_divisor(j0)), 0 < i2, 0 < max_prime_divisor(j0) * max_prime_divisor(j0), i0 ≤ 0, i0 < j0, i0 < i, i0 < i2, i0 < max_prime_divisor(j0) * max_prime_divisor(j0), ∀ j1, j, i. i→n(j1) < i→n(j0) → j1 * j1 = j * i * i ∧ 0 < j1 ∧ 0 < j ∧ 0 < i → i = 0 ∨ isSquare(j) ⊦ max_prime_divisor(j0) = 0, i = 0, prime(j0), isSquare(max_prime_divisor(j0) * max_prime_divisor(j0) * i2), max_prime_divisor(j0) | i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: mult-pos seq: ⊦ 0 ≤ i ∧ 0 < j ∧ i1 < 0 → i * i1 ≠ j subst: [j, i1, i] → [j0, i0, max_prime_divisor(j0)] flags: rewrite

Additional information

Used simplifier rules: prime-not-neg: ⊦ j < 0 → ¬ prime(j);%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult%zero-left: ⊦ 0 * i = 0; from specification int-mult%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1 Used terms: j0, i0, max_prime_divisor(j0)