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Proof step 24 from proof byte-law-and-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ b2i(i2b(i)) = bits2int(lastn(8, fillsgn(8, int2bits(i))))
Proof step 26:
lastn(8, fillsgn(8, int2bits(i))) ≠ [] ∧ int2bits(j) ≠ [], bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j)) ≠ [], lastn(8, fillsgn(8, int2bits(i))) ≠ [] ⊦ bits2int(bitsand(int2bits(i), int2bits(j))) = bits2int(bitsand(sgn(lastn(8, fillsgn(8, int2bits(i)))), int2bits(j))), bits2int(lastn(8, fillsgn(8, int2bits(bits2int(bitsand(int2bits(i), int2bits(j))))))) = bits2int(lastn(8, fillsgn(8, sgn(bitsand(lastn(8, fillsgn(8, int2bits(i))), int2bits(j))))))

Rule argument

name: bib-on-bits rotate: F subst: [i] → [bits2int(bitsand(int2bits(i), int2bits(j)))]

Additional information

Used terms: bits2int(bitsand(int2bits(i), int2bits(j)))