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Proof step 26 from proof mult-eq-same (previous step)

i * 10 ^ abs(i2) * 10 ^ abs(i4) = i1 * 10 ^ abs(i0) * 10 ^ abs(i4) ⊦ i3 = 0, mkDecimal(i3, i4) = mkDecimal(0, 0), mkDecimal(i, i0) = mkDecimal(i1, i2)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 27:
⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0)
Proof step 28:
10 ^ abs(i4) ≠ 0 → (10 ^ abs(i4) * i * 10 ^ abs(i2) = 10 ^ abs(i4) * i1 * 10 ^ abs(i0) ↔ i * 10 ^ abs(i2) = i1 * 10 ^ abs(i0)), i * 10 ^ abs(i2) * 10 ^ abs(i4) = i1 * 10 ^ abs(i0) * 10 ^ abs(i4) ⊦ i3 = 0, mkDecimal(i3, i4) = mkDecimal(0, 0), mkDecimal(i, i0) = mkDecimal(i1, i2)

Rule argument

spec: int-mult inst: name: eq-nonzero seq: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0) subst: [i, j, j0] → [10 ^ abs(i4), i * 10 ^ abs(i2), i1 * 10 ^ abs(i0)] flags: []

Additional information

Used terms: 10 ^ abs(i4), i * 10 ^ abs(i2), i1 * 10 ^ abs(i0)