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Proof step 8 from proof cast-band (previous step)

# int2bits(j0) = m + 1, n→i(m) ≤ i, 0 ≤ j0 ⊦ band(bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), j0) = bits2int(bitsand(int2bits(j), int2bits(j0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j)))
Proof step 10:
# int2bits(j0) = m + 1, n→i(m) ≤ i, 0 ≤ j0 ⊦ bits2int(bitsand(int2bits(bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))))), int2bits(j0))) = bits2int(bitsand(int2bits(j), int2bits(j0)))

Rule argument

name: band-def rotate: F subst: [j, i] → [j0, bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))))]

Additional information

Used terms: j0, bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))))