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Proof step 91 from proof getsetShort-theorem (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: bib-pos-low: ⊦ 0 ≤ i ∧ i % 256 ≤ 127 → b2i(i2b(i)) = i % 256;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%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%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: ⊦ i = i + j ↔ j = 0; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%mod-nle-01: ⊦ 0 < j ∧ 0 ≤ i ∧ j ≤ i0 → ¬ i0 ≤ i % j; from specification int-div Used terms: j