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Proof step 28 from proof mult-eq-same (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: absls: ⊦ ¬ abs(i) < 0; from specification int-abs%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%eq-nonzero: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0); from specification int-mult