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Proof step 31 from proof add-scale-neq (previous step)

(dec_i.int + dec_j.int) % 10 = 0, dec_i.int + dec_j.int * 10 ^ (dec_i.scale - dec_j.scale + 1) * 10 = 0, 0 < dec_j.scale, 1 < dec_i.scale, 0 ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 < dec_i.scale, dec_j.scale < dec_i.scale ⊦ dec_j.scale = 0, dec_i.int % 10 = 0, dec_i.scale = dec_j.scale

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ i + j = i0 ↔ i = i0 - j
Proof step 33:
(dec_i.int + dec_j.int) % 10 = 0, dec_i.int = 0 - dec_j.int * 10 ^ (dec_i.scale - dec_j.scale + 1) * 10, 0 < dec_j.scale, 1 < dec_i.scale, 0 ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 < dec_i.scale, dec_j.scale < dec_i.scale ⊦ dec_j.scale = 0, dec_i.int % 10 = 0, dec_i.scale = dec_j.scale

Rule argument

spec: int-abs inst: name: add-shift seq: ⊦ i + j = i0 ↔ i = i0 - j subst: [i0, j, i] → [0, dec_j.int * 10 ^ (dec_i.scale - dec_j.scale + 1) * 10, dec_i.int] flags: rewrite

Additional information

Used terms: 0, dec_j.int * 10 ^ (dec_i.scale - dec_j.scale + 1) * 10, dec_i.int