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Proof step 22 from proof fits-law-shr-01 (previous step)

s2i(sho) ≤ s2i(sho) i>> band(i, 31), s2i(sho) i>> band(i, 31) ≤ 0, s2i(sho) ≤ 0 ⊦ s2i(sho) i>> band(i, 31) = s2i(i2s(s2i(sho) i>> band(i, 31)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i

Rule argument

name: num-issi rotate: F subst: [i] → [s2i(sho) i>> band(i, 31)]

Additional information

Used simplifier rules: short-min-01: ⊦ ¬ s2i(sho) < ~32768;% ⊦ ¬ i ≤ j ↔ j < i;%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0);% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) Used terms: s2i(sho) i>> band(i, 31)