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Proof step 4 from proof short-011x-neg (previous step)

s2i(sho) < 0 ⊦ band(s2i(sho), 2 ^ 16 - 1) = s2i(sho) + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ j < 0 ∧ 0 ≤ i → band(j, 2 ^ i - 1) = (j + 1) % 2 ^ i + 2 ^ i - 1
Proof step 6:
s2i(sho) < 0 ∧ 0 ≤ 16, s2i(sho) < 0 ⊦ (s2i(sho) + 1) % 2 ^ 16 + 2 ^ 16 - 1 = s2i(sho) + 65536

Rule argument

seq: ⊦ j < 0 ∧ 0 ≤ i → band(j, 2 ^ i - 1) = (j + 1) % 2 ^ i + 2 ^ i - 1 subst: [i, j] → [16, s2i(sho)] rotate: F spec: intops inst: name: band-011x-neg

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 16, s2i(sho)