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Proof step 40 from proof add-scale-neq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
(dec_i.int - dec_i.int * 10 ^ (dec_j.scale - dec_i.scale)) % 10 = 0, 0 < dec_i.scale, 1 < dec_j.scale, 0 ≤ dec_j.scale, dec_i.scale < dec_j.scale, 0 ≤ dec_i.scale + dec_j.scale, 0 < dec_j.scale ⊦ dec_i.scale = 0, (dec_i.int * 10 ^ (dec_j.scale - dec_i.scale)) % 10 = 0

Rule argument

Additional information

Used simplifier rules: neg-10: ⊦ ~ i = 0 ↔ i = 0; from specification int-abs%mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j); from specification int-div%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%neg-06: ⊦ 0 - i = ~ i; from specification int-abs