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Proof step 750 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 751:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 752:
¬ # bits1 ≤ #(bitsand(bits2, bits4) + bitsand(false ' + true ' + bits, bits1)), 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits) ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits4) + bitsand(false ' + true ' + bits, bits1)))
Proof step 755:
# bits1 ≤ #(bitsand(bits2, bits4) + bitsand(false ' + true ' + bits, bits1)), 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits) ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(bits2, bits4) + bitsand(false ' + true ' + bits, bits1))

Rule argument

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

Additional information

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