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Proof step 12 from proof mult-eq-same (previous step)

mkDecimal(i * i3, abs(i0) + abs(i4)) = mkDecimal(i1 * i3, abs(i2) + abs(i4)) ⊦ mkDecimal(i3, i4) = mkDecimal(0, 0), mkDecimal(i, i0) = mkDecimal(i1, i2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ mkDecimal(i, j) = mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) = i0 * 10 ^ abs(j)
Proof step 14:
(i * i3) * 10 ^ abs(abs(i2) + abs(i4)) = (i1 * i3) * 10 ^ abs(abs(i0) + abs(i4)) ⊦ mkDecimal(i3, i4) = mkDecimal(0, 0), mkDecimal(i, i0) = mkDecimal(i1, i2)

Rule argument

spec: decimal inst: name: equality-any seq: ⊦ mkDecimal(i, j) = mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) = i0 * 10 ^ abs(j) subst: [j0, i0, j, i] → [abs(i2) + abs(i4), i1 * i3, abs(i0) + abs(i4), i * i3] flags: rewrite

Additional information

Used terms: abs(i2) + abs(i4), i1 * i3, abs(i0) + abs(i4), i * i3