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Proof step 27 from proof maxScale-pot10-add (previous step)

min(j, j0) < 0, 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 * 10 ^ j + i0 * 10 ^ j0 = (i * 10 ^ (j - min(j, j0))) * 10 ^ min(j, j0) + i0 * 10 ^ (j0 - min(j, j0)) * 10 ^ min(j, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-min inst: name: Min-right seq: ⊦ ¬ j < i → min(j, i) = i subst: [i, j] → [j0, j] flags: rewrite

Additional information

Used simplifier rules: sub-sub-03: ⊦ i - i = 0; from specification int-abs%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-in: ⊦ i + j = i + i0 ↔ j = i0; 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%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%Min-left: ⊦ j < i → min(j, 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: j0, j