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Proof step 16 from proof getsetShort-theorem (previous step)

j < 0, 0 ≤ ub2i(i2b(j)), ub2i(i2b(j)) < 256, ~32768 ≤ j ⊦ ub2i(i2b(j)) + 256 * b2i(i2b(j >> 8)) = j, (j >> 8)∈byte

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ i < 0 ∧ 8 ≤ j → i >> j = (i - 255) / 256 >> (j - 8)
Proof step 18:
j < 0 ∧ 8 ≤ 8, j < 0, 0 ≤ ub2i(i2b(j)), ub2i(i2b(j)) < 256, ~32768 ≤ j ⊦ ub2i(i2b(j)) + 256 * b2i(i2b((j - 255) / 256 >> (8 - 8))) = j, ((j - 255) / 256 >> (8 - 8))∈byte

Rule argument

spec: intops inst: name: shiftright-rec-8-neg seq: ⊦ i < 0 ∧ 8 ≤ j → i >> j = (i - 255) / 256 >> (j - 8) subst: [j, i] → [8, j] flags: rewrite

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: 8, j