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Proof step 837 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [ (bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0), 2 + # bits + m] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: (bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0), 2 + # bits + m