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Proof step 16 from proof cast-law-and-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits)
Proof step 18:
¬ bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0)) ≠ [], 0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), bitsand(int2bits(j), int2bits(j0))))) = bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(bits2int(bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0)))))))
Proof step 21:
bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0)) ≠ [], 0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), bitsand(int2bits(j), int2bits(j0))))) = bits2int(lastn(i→n(i), fillsgn(i→n(i), sgn(bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0))))))

Rule argument

seq: bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits) subst: [bits] → [bitsand (sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0))] rotate: F spec: int2bits inst: name: bits2bits-def

Additional information

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