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Proof step 854 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, bits0.first, # bits0 ≤ 2 + # bits, # bits0 ≤ (2 + # bits) + # bits2, 2 + # bits ≤ # bitsand(boolvar ' + boolvar0 ' + bits, bits0), # bits0 ≤ # bitsand(boolvar ' + boolvar0 ' + bits, bits0) ⊦ boolvar ↔ boolvar0, lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(2 + # bits + m, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), bits0 = [], boolvar ∧ boolvar0

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] → [bitsand(boolvar ' + boolvar0 ' + bits, bits0), 2 + # bits + m] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used terms: bitsand(boolvar ' + boolvar0 ' + bits, bits0), 2 + # bits + m