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Proof step 15 from proof maxScale-pot10-add (previous step)

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

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: [i, i0, j0, j] → [i0, i, j - j0, 10] 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%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%sub-eq-01: ⊦ i = j → i - j = 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-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i0, i, j - j0, 10