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Proof step 33 from proof add-scale-neq (previous step)

(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

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 2 flags: discard

Additional information

Used simplifier rules: neg-06: ⊦ 0 - i = ~ i; from specification int-abs%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j); from specification int-div%mod-zero-num: i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult