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Proof step 71 from proof getsetShort-theorem (previous step)

j / 256 = i + 1, j < 0, ~32768 ≤ j, ~128 ≤ i, i ≤ 127, ~256 ≤ b2i(i2b(j)), b2i(i2b(j)) < 0 ⊦ j % 256 = 0, 256 * (i + 1) + b2i(i2b(j)) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 72:
⊦ i < 0 ∧ ~128 ≤ i % 256 → b2i(i2b(i)) = i % 256
Proof step 73:
j < 0 ∧ ~128 ≤ j % 256, j / 256 = i + 1, j < 0, ~32768 ≤ j, ~128 ≤ i, i ≤ 127, ~256 ≤ j % 256, j % 256 < 0 ⊦ j % 256 = 0, 256 * (i + 1) + j % 256 = j

Rule argument

spec: inst: name: bib-neg-high seq: ⊦ i < 0 ∧ ~128 ≤ i % 256 → b2i(i2b(i)) = i % 256 subst: [i] → [j] flags: rewrite, current

Additional information

Used simplifier rules: bib-neg-low: ⊦ i < 0 ∧ i % 256 < ~128 → b2i(i2b(i)) = i % 256 + 256;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%succ-rmerge: ⊦ i * j + i = i * (j + 1); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%mod-lsz: ⊦ 0 < j → ¬ j + i % j < 0; from specification int-div Used terms: j