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Proof step 4 from proof band-sis (previous step)

band(s2i(i2s(i)), s2i(i2s(j))) = s2i(i2s(band(s2i(i2s(i)), s2i(i2s(j))))), ~32768 ≤ i, i ≤ 32767, ~32768 ≤ j, j ≤ 32767 ⊦ s2i(i2s(band(i, j))) = band(i, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i
Proof step 6:
~32768 ≤ i ∧ i ≤ 32767, band(i, s2i(i2s(j))) = s2i(i2s(band(i, s2i(i2s(j))))), ~32768 ≤ i, i ≤ 32767, ~32768 ≤ j, j ≤ 32767 ⊦ s2i(i2s(band(i, j))) = band(i, j)

Rule argument

name: num-issi rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0); Used terms: i