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Proof step 9 from proof add-scale-neq (previous step)

maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale), maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale) ⊦ abs(dec_i.scale + dec_j.scale) - maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) = max(dec_i.scale, dec_j.scale), dec_i.scale = dec_j.scale

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale) ⊦ dec_i.scale = dec_j.scale, abs(dec_i.scale + dec_j.scale) = max(dec_i.scale, dec_j.scale) + maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale)

Rule argument

Additional information

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