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Proof step 36 from proof getsetShort-theorem (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: forward-lele seq: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1 subst: [j, j0, j1] → [256, i * 256, 255 + j] flags: rewrite

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%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%nummult-le-02: ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0); from specification int-div%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); from specification int-abs Used terms: 256, i * 256, 255 + j