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Proof step 11 from proof maxScale-pot10-add (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
(i + i0 * 10 ^ (j0 - j)) % 10 = 0, j < j0, 0 ≤ j0, 0 ≤ j, 0 < j0 ⊦ i % 10 = 0, i0 % 10 = 0, (i + i0) % 10 = 0, maxScale((i + i0 * 10 ^ (j0 - j)) * 10 ^ j) = j

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%sub-sub-03: ⊦ i - i = 0; from specification int-abs%min-c: ⊦ min(i, j) = min(j, i); from specification int-min%min-a: ⊦ min(i, min(j, j0)) = min(min(i, j), j0); from specification int-min%Min-left: ⊦ j < i → min(j, i) = j; from specification int-min