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Proof step 22 from proof pot-isSquare (previous step)

0 < j, 0 < j0 * j0 ⊦ (j0 * j0) ^ j = j0 ^ j * j0 ^ j, isSquare((j0 * j0) ^ j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [j, j, j0] flags: rewrite

Additional information

Used simplifier rules: add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%pot-square-02: ⊦ 0 ≤ j → ((i * i) ^ j ≠ i ^ (2 * j) ↔ false); from specification int-pot%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j, j, j0