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Proof step 30 from proof add-scale-neq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
(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

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs%sub-pred: ⊦ i -1 = i - 1; from specification int-abs