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Proof step 16 from proof fits-law-shr-01 (previous step)

s2i(sho) i>> band(i, 31) ≤ s2i(sho), 0 < s2i(sho), 0 ≤ s2i(sho) i>> band(i, 31), 0 ≤ s2i(sho) ⊦ 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 17:
~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-max-10: ⊦ 32767 < i → s2i(sho) ≠ i;%short-ngr: ⊦ ¬ 32767 < s2i(sho);%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) Used terms: s2i(sho) i>> band(i, 31)