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Proof step 30 from proof maxScale-pot10-add (previous step)

0 ≤ min(j, j0), min(j, j0) ≤ j0, 0 ≤ j0, 0 ≤ j ⊦ i % 10 = 0, i0 % 10 = 0, (i + i0) % 10 = 0, maxScale(i * 10 ^ j + i0 * 10 ^ j0) = min(j, j0), i = 0, 10 ^ j = 10 ^ (j - min(j, j0)) * 10 ^ min(j, j0)

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] → [min(j, j0), j - min(j, j0), 10] flags: rewrite

Additional information

Used simplifier rules: Sub-def: ⊦ i + (j - i) = j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%eq-pos: ⊦ 1 < i0 ∧ 0 ≤ i ∧ 0 ≤ j → (i0 ^ i = i0 ^ j ↔ i = j); from specification int-pot%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%min-03: ⊦ ¬ i < min(i, j); from specification int-min%min-a: ⊦ min(i, min(j, j0)) = min(min(i, j), j0); from specification int-min%min-c: ⊦ min(i, j) = min(j, i); from specification int-min Used terms: min(j, j0), j - min(j, j0), 10