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Proof step 56 from proof square-neq-any-pos-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: not-less-gcd seq: ⊦ 0 < i → ¬ i < gcd(i, j) subst: [j, i] → [j, j0 * j1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < j → ¬ j < i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, j0 * j1