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Proof step 11 from proof cast-law-and-one (previous step)

0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), bitsand(int2bits(j), int2bits(j0))))) = cast(i, band(bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), j0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j)))
Proof step 13:
0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), bitsand(int2bits(j), int2bits(j0))))) = cast(i, bits2int(bitsand(int2bits(bits2int(lastn(i→n(i), fillsgn(i→n(i), 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))))