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Proof step 24 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), sgn(bitsand(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))), int2bits(j0)))))), bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0)) = [], i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ bits ≠ [] → lastn(n, fillsgn(n, sgn(bits))) = lastn(n, fillsgn(n, bits))
Proof step 26:
¬ bitsand(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(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))), int2bits(j0)))))), bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0)) = [], i = 0
Proof step 29:
bitsand(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), bitsand(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))), int2bits(j0))))), bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0)) = [], i = 0

Rule argument

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

Additional information

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