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Proof step 8 from proof mkDecimal-maxScale-le (previous step)

maxScale(i) ≤ abs(j), maxScale(i) ≤ abs(j), maxScale(i) ≤ abs(j) ⊦ i / 10 ^ maxScale(i) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).int ∧ abs(j) - maxScale(i) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).scale

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
maxScale(i) ≤ abs(j) ⊦ i / 10 ^ maxScale(i) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).int ∧ abs(j) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).scale + maxScale(i)

Rule argument

Additional information

Used simplifier rules: sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs