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Proof step 55 from proof getsetShort-theorem (previous step)

j < 0, 0 ≤ ub2i(i2b(j)), j i>> 8 ≤ 127, ~128 ≤ j i>> 8, ub2i(i2b(j)) < 256, ~32768 ≤ j ⊦ ub2i(i2b(j)) + 256 * (j i>> 8) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ i < 0 ∧ i % 256 = 0 → i i>> 8 = i / 256
Proof step 57:
¬(j < 0 ∧ j % 256 = 0), j < 0, 0 ≤ ub2i(i2b(j)), j i>> 8 ≤ 127, ~128 ≤ j i>> 8, ub2i(i2b(j)) < 256, ~32768 ≤ j ⊦ ub2i(i2b(j)) + 256 * (j i>> 8) = j
Proof step 75:
j < 0 ∧ j % 256 = 0, j < 0, 0 ≤ ub2i(i2b(j)), j / 256 ≤ 127, ~128 ≤ j / 256, ub2i(i2b(j)) < 256, ~32768 ≤ j ⊦ ub2i(i2b(j)) + 256 * j / 256 = j

Rule argument

spec: intops inst: name: intshiftrsign-neg-01 seq: ⊦ i < 0 ∧ i % 256 = 0 → i i>> 8 = i / 256 subst: [i] → [j] flags: rewrite

Additional information

Used terms: j