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Proof step 15 from proof byte-law-and-one (previous step)

lastn(8, fillsgn(8, int2bits(i))) ≠ [] ⊦ band(i, j) = bits2int(bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j))), b2i(i2b(band(i, j))) = bits2int(lastn(8, fillsgn(8, int2bits(bits2int(bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j)))))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits)
Proof step 17:
¬ bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j)) ≠ [], lastn(8, fillsgn(8, int2bits(i))) ≠ [] ⊦ band(i, j) = bits2int(bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j))), b2i(i2b(band(i, j))) = bits2int(lastn(8, fillsgn(8, int2bits(bits2int(bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j)))))))
Proof step 20:
bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j)) ≠ [], lastn(8, fillsgn(8, int2bits(i))) ≠ [] ⊦ band(i, j) = bits2int(bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j))), b2i(i2b(band(i, j))) = bits2int(lastn(8, fillsgn(8, sgn(bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j))))))

Rule argument

seq: bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits) subst: [bits] → [bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j))] rotate: F spec: int2bits inst: name: bits2bits-def

Additional information

Used terms: bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j))