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Proof step 55 from proof add-scale-neq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
(dec_i.int + dec_j.int) % 10 = 0, (dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int) % 10 = 0, 0 ≤ dec_i.scale, dec_i.scale < dec_j.scale, 0 ≤ dec_j.scale, maxScale(dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int) ≤ dec_j.scale, 0 < dec_j.scale ⊦ dec_j.int % 10 = 0, dec_i.int % 10 = 0, maxScale(dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int) = 0, dec_i.int * 10 ^ (dec_j.scale - dec_i.scale) + dec_j.int = 0

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%le-add: ⊦ i + j ≤ i0 + j ↔ i ≤ i0; from specification int-abs%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%add-c: ⊦ i + j = j + i; from specification int-basic2%eq: ⊦ i = i + j ↔ j = 0; from specification int-basic2%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%max-c: ⊦ max(i, j) = max(j, i); from specification int-min%max-a: ⊦ max(i, max(j, j0)) = max(max(i, j), j0); from specification int-min%Max-left: ⊦ ¬ j < i → max(j, i) = j; from specification int-min%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%sub-sub-03: ⊦ i - i = 0; from specification int-abs