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Proof step 11 from proof add-scale-eq (previous step)

dec_i.scale = dec_j.scale, maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale) ≤ 2 * abs(dec_j.scale), dec_j.scale + maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale) < 2 * abs(dec_j.scale) ⊦ dec_i.int + dec_j.int = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬ j < 0 → abs(j) = j
Proof step 13:
¬ dec_j.scale < 0, dec_i.scale = dec_j.scale, maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale) ≤ 2 * dec_j.scale, dec_j.scale + maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale) < 2 * dec_j.scale ⊦ dec_i.int + dec_j.int = 0

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [dec_j.scale] flags: rewrite

Additional information

Used simplifier rules: scale-not-neg: ⊦ ¬ dec.scale < 0; from specification decimal Used terms: dec_j.scale