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Proof step 44 from proof getsetShort-theorem (previous step)

ub2i(i2b(j)) < 256, 0 ≤ ub2i(i2b(j)), 0 ≤ j, j < 32768 ⊦ 256 * b2i(i2b(j / 256)) + ub2i(i2b(j)) = j, ~128 ≤ j / 256 ∧ j / 256 ≤ 127

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
0 < j / 256, 127 < j / 256, j < 32768, 0 ≤ j, 0 ≤ ub2i(i2b(j)), ub2i(i2b(j)) < 256 ⊦ 256 * b2i(i2b(j / 256)) + ub2i(i2b(j)) = j

Rule argument

Additional information

Used simplifier rules: numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%zero-gels: ⊦ i < 0 ∧ 0 ≤ j → ¬ j < i; from specification int-abs%num-ls: ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0); from specification int-div%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs