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Proof step 88 from proof getsetShort-theorem (previous step)

b2i(i2b(j)) < 0, ~256 ≤ b2i(i2b(j)), j / 256 ≤ 127, ~128 ≤ j / 256, j ≤ 32767, 0 ≤ j, 128 ≤ j, 0 < j ⊦ 256 * (j / 256 + 1) + b2i(i2b(j)) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: bib-pos-low seq: ⊦ 0 ≤ i ∧ i % 256 ≤ 127 → b2i(i2b(i)) = i % 256 subst: [i] → [j] flags: rewrite, current

Additional information

Used simplifier rules: bib-pos-high: ⊦ 0 ≤ i ∧ 127 < i % 256 → b2i(i2b(i)) = i % 256 - 256;%mod-ls-zero: 0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0; from specification int-div%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%sub-add-01: ⊦ i + (j - i0) = i + j - i0; 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%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%eq-succ: ⊦ i * (i0 + 1) + j = i + j0 ↔ i * i0 + j = j0; from specification int-mult%divmod-rew: j ≠ 0 ⊦ i / j * j + i % j = i; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j