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Proof step 7 from proof bitsand-cast-05 (previous step)

⊦ bits = [], sgn(bitsand(lastn(# bits1, fillsgn(# bits1, bits)), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 9:
¬ # bits1 ≤ # bits ⊦ bits = [], sgn(bitsand(lastn(# bits1, fillsgn(# bits1, bits)), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits1 = []
Proof step 27:
# bits1 ≤ # bits ⊦ bits = [], sgn(bitsand(lastn(# bits1, bits), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits1 = []

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [bits, # bits1] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: bits, # bits1