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Proof step 9 from proof square-neq-any-pos (previous step)

j * j = i * j0 * j0, j < i, j < 0, 0 < i, j + 1 < i, j0 ≤ 0, j0 < i ⊦ j = 0, ∃ i0. i = i0 * i0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: square-neq-any-pos-01 seq: 0 < i, 0 < j, 0 < j0, j * j = i * j0 * j0 ⊦ ∃ i0. i = i0 * i0 subst: [i, j, j0] → [i, ~ j, ~ j0] flags: current, []

Additional information

Used simplifier rules: neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%minus-left: ⊦ ~ i * j = ~(i * 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%neg-02: ⊦ ~ ~ i = i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%zero-left: ⊦ 0 * i = 0; from specification int-mult%zero-neq: ⊦ i < 0 → (i * j = 0 ↔ j = 0); from specification int-mult Used terms: i, ~ j, ~ j0