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Proof step 2 from proof bitsand-cast-01 (previous step)

⊦ bits = [], bits0 = [], lastn(n, fillsgn(n, bitsand(lastn(n, fillsgn(n, bits)), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 4:
¬ n ≤ # bits ⊦ bits = [], bits0 = [], lastn(n, fillsgn(n, bitsand(lastn(n, fillsgn(n, bits)), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0)))
Proof step 10:
n ≤ # bits ⊦ bits = [], bits0 = [], lastn(n, fillsgn(n, bitsand(lastn(n, bits), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0)))

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [bits, n] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: bits, n