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Proof step 33 from proof getsetShort-theorem (previous step)

~128 = i + i0, i0 < 0, j ≤ 0, i0 * 256 + j < 0, 0 ≤ ub2i(i2b(j + 255)), i0 < i + i0, abs(j) < 256, i0 * 256 + j ≤ ~256, ub2i(i2b(j + 255)) < 256, i * 256 ≤ 255 + j ⊦ ub2i(i2b(j + 255)) + 256 * b2i(i2b(i0)) = (i0 * 256 + j) + 255

User applied rule cut formula

And obtained the following new goals

Proof step 34:
0 < i, ~128 = i + i0, i0 < 0, j ≤ 0, i0 * 256 + j < 0, 0 ≤ ub2i(i2b(j + 255)), i0 < i + i0, abs(j) < 256, i0 * 256 + j ≤ ~256, ub2i(i2b(j + 255)) < 256, i * 256 ≤ 255 + j ⊦ ub2i(i2b(j + 255)) + 256 * b2i(i2b(i0)) = (i0 * 256 + j) + 255

Rule argument

fma: 0 < i

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%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used formulas: 0 < i