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Proof step 24 from proof add-a (previous step)

⊦ mkDecimal(i * 10 ^ abs(i2) * 10 ^ abs(i4) + (i1 * 10 ^ abs(i4)) * 10 ^ abs(i0) + (i3 * 10 ^ abs(i2)) * 10 ^ abs(i0), abs(i0) + abs(i2) + abs(i4)) = mkDecimal(((i * 10 ^ abs(i2)) * 10 ^ abs(i4) + (i1 * 10 ^ abs(i0)) * 10 ^ abs(i4)) + i3 * 10 ^ (abs(i0) + abs(i2)), (abs(i0) + abs(i2)) + abs(i4))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [abs(i2), abs(i0), 10] flags: rewrite

Additional information

Used simplifier rules: 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%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs Used terms: abs(i2), abs(i0), 10