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Proof step 5 from proof add-scale-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = 0
Proof step 7:
¬ ¬ maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale) ≤ abs(2 * dec_j.scale), dec_i.scale = dec_j.scale, dec_j.scale < mkDecimal(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale, 2 * dec_j.scale).scale ⊦ dec_i.int + dec_j.int = 0

Rule argument

spec: decimal inst: name: mkDecimal-maxScale-nle-scale seq: ⊦ ¬ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = 0 subst: [j, i] → [2 * dec_j.scale, dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale] flags: rewrite

Additional information

Used simplifier rules: scale-not-neg: ⊦ ¬ dec.scale < 0; from specification decimal Used terms: 2 * dec_j.scale, dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_j.scale