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Proof step 61 from proof isSquare-mult-aux (previous step)

i0 * i0 = i1 * i1 * j, max_prime_divisor(j0) * i0 = j0, max_prime_divisor(j0) * i0 ≤ i0, 0 < max_prime_divisor(max_prime_divisor(j0) * i0) * i1, 0 < max_prime_divisor(j0) * i0, 0 < j, prime(max_prime_divisor(max_prime_divisor(j0) * i0)), 0 < i0, ∀ j1, j, i. i→n(j1) < i→n(max_prime_divisor(j0) * i0) → j1 * j1 = j * i * i ∧ 0 < j1 ∧ 0 < j ∧ 0 < i → i = 0 ∨ isSquare(j) ⊦ max_prime_divisor(max_prime_divisor(j0) * i0) = 0, i1 = 0, prime(max_prime_divisor(j0) * i0), isSquare(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numle-07 seq: ⊦ (* i1) * j ≤ j ↔ 0 ≤ (1 - i1) * j subst: [j, i1] → [i0, max_prime_divisor(j0)] flags: rewrite

Additional information

Used simplifier rules: prime-small: ⊦ j < 2 → ¬ prime(j);%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs Used terms: i0, max_prime_divisor(j0)