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Proof step 16 from proof add-scale-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: decimal inst: name: maxScale-pot10-nls seq: ⊦ 0 ≤ j ∧ i ≠ 0 → ¬ maxScale(i * 10 ^ j) < j subst: [j, i] → [dec_j.scale, dec_i.int + dec_j.int] flags: rewrite

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%scale-not-neg: ⊦ ¬ dec.scale < 0; from specification decimal Used terms: dec_j.scale, dec_i.int + dec_j.int