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Proof step 492 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits ⊦ bits4 = [], bits2 = [], lastn(# bits1, fillsgn(# bits1, bits4 + bitsand(bits1, true ' + false ' + bits))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits4 + bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 493:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 494:
¬ # bits1 ≤ #(bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits)), # bits1 = 2 + # bits ⊦ bits4 = [], bits2 = [], lastn(# bits1, fillsgn(# bits1, bits4 + bitsand(bits1, true ' + false ' + bits))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits4 + bits1 = []
Proof step 497:
# bits1 ≤ #(bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits)), # bits1 = 2 + # bits ⊦ bits4 = [], bits2 = [], lastn(# bits1, fillsgn(# bits1, bits4 + bitsand(bits1, true ' + false ' + bits))) = lastn(# bits1, bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits)), bits1 = [], bits4 + bits1 = []

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [ bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits), # bits1] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits), # bits1