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Proof step 12 from proof maxScale-pot10-add (previous step)

(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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-mod-add-zero seq: ⊦ 0 ≤ j ∧ 0 < j0 → ((i + i0 * j ^ j0) % j = 0 ↔ i % j = 0) subst: [j0, j, i0, i] → [j0 - j, 10, i0, i] flags: rewrite

Additional information

Used simplifier rules: sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%add-zero: ⊦ i + 0 = 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 Used terms: j0 - j, 10, i0, i