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Proof step 68 from proof add-scale-neq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
⊦ dec.scale ≠ 0 → dec.int % 10 ≠ 0
Proof step 70:
¬ dec_i.scale ≠ 0, dec_i.int % 10 = 0, maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ dec_j.scale ⊦ dec_i.scale = dec_j.scale, dec_i.scale + dec_j.scale = max(dec_i.scale, dec_j.scale) + maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale)

Rule argument

spec: decimal inst: name: intvalue-mod-10 seq: ⊦ dec.scale ≠ 0 → dec.int % 10 ≠ 0 subst: [dec] → [dec_i] flags: rewrite

Additional information

Used terms: dec_i