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Proof step 163 from proof bitsand-cast (previous step)

n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, (mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1), sgn((mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1) = true ' + false ' + bits1, bits2.first, 2 + # bits1 + n < n0 + # bits ⊦ mklist(true, n0) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n0 + # bits2 + # bits, mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1)), bits2 = [], bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits = [], bits2 + bits = [], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [ mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1), n0 + # bits2 + # bits] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used terms: mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1), n0 + # bits2 + # bits