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Proof step 7 from proof square-neq-prime (previous step)

j * j = i * j0 * j0, j0 < j, j0 < 0, 0 < j, prime(i), j0 + 1 < j ⊦ j = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: square-neq-pos seq: ⊦ prime(i) ∧ 0 < j ∧ 0 ≤ j0 → j * j ≠ i * j0 * j0 subst: [i, j, j0] → [i, j, ~ j0] flags: current, []

Additional information

Used simplifier rules: negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; 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%zero-gels-03: ⊦ 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 Used terms: i, j, ~ j0