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Proof step 56 from proof add-scale-neq (previous step)

(dec_i.int + dec_j.int) % 10 = 0, (dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int) % 10 = 0, 0 ≤ dec_i.scale, dec_i.scale < dec_j.scale, 0 ≤ dec_j.scale, maxScale(dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int) ≤ dec_j.scale, 0 < dec_j.scale ⊦ dec_j.int % 10 = 0, dec_i.int % 10 = 0, maxScale(dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int) = 0, dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int = 0

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] → [dec_j.int, dec_i.int, dec_j.scale - dec_i.scale, 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%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: dec_j.int, dec_i.int, dec_j.scale - dec_i.scale, 10