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Proof step 65 from proof add-scale-neq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: decimal inst: name: maxScale-base seq: ⊦ i % 10 ≠ 0 ∧ i ≠ 0 → maxScale(i) = 0 subst: [i] → [dec_i.int + dec_j.int * 10 ^ dec_i.scale] flags: rewrite

Additional information

Used simplifier rules: pot-mod-add-zero: ⊦ 0 ≤ j ∧ 0 < j0 → ((i + i0 * j ^ j0) % j = 0 ↔ i % j = 0); from specification int-pot%intvalue-mod-10: ⊦ dec.scale ≠ 0 → dec.int % 10 ≠ 0; from specification decimal%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%maxScale-zero: ⊦ maxScale(0) = 0; from specification decimal Used terms: dec_i.int + dec_j.int * 10 ^ dec_i.scale