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Proof step 50 from proof square-neq-any-pos-02 (previous step)

gcd(j, j0) = 1, j * j / gcd(j0 * j1, j) = (j0 * j1) * (j0 * j1) / gcd(j0 * j1, j) * i, j / gcd(j, j0 * j1) * j / gcd(j0 * j1, j) = (j0 * j1) / gcd(j0 * j1, j) * (j0 * j1) / gcd(j0 * j1, j) * i, j1 * j1 ≤ 1, 0 < j1, 0 < j0, 0 < j, 0 ≤ j0, 1 < j1 * j1 * i, prime(j1), j1 * j1 < i, 1 < i, 0 < i, ∀ i1, j, j0. i→n(i1) < i→n(j1 * j1 * i) → 0 < i1 ∧ 0 < j ∧ 0 < j0 ∧ gcd(j, j0) = 1 ∧ j * j = i1 * j0 * j0 → (∃ i2. i1 = i2 * i2) ⊦ j = 0, j1 = 0, gcd(j0 * j1, j) = 1, ∃ i1. j1 * j1 * i = i1 * i1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: le-one seq: ⊦ 1 < j → (i * j ≤ 1 ↔ i ≤ 0) subst: [j, i] → [j1, j1] flags: rewrite

Additional information

Used simplifier rules: gcd-com: ⊦ gcd(i, j) = gcd(j, i);%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%one-01: ⊦ i = 1 → i * j = 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 Used terms: j1, j1