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Proof step 77 from proof add-scale-neq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-add-min seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i * 10 ^ j + i0 * 10 ^ j0 = (i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) * 10 ^ min(j, j0) subst: [j0, i0, j, i] → [dec_i.scale, dec_j.int, dec_j.scale, dec_i.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_i.scale, dec_j.int, dec_j.scale, dec_i.int