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Proof step 7 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) ⊦ mkDecimal(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale, dec_i.scale + dec_j.scale).scale = max(dec_i.scale, dec_j.scale), dec_i.scale = dec_j.scale

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = abs(j) - maxScale(i)
Proof step 9:
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

Rule argument

spec: decimal inst: name: mkDecimal-maxScale-le-scale seq: ⊦ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = abs(j) - maxScale(i) subst: [j, i] → [dec_i.scale + dec_j.scale, dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale] flags: rewrite

Additional information

Used terms: dec_i.scale + dec_j.scale, dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale