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Proof step 846 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 ⊦ boolvar ↔ boolvar0, lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(2 + # bits + m, (bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), bits0 = [], boolvar ∧ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 847:
⊦ (bits + bits0) + bits1 = bits + bits0 + bits1
Proof step 848:
sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, bits0.first, # bits0 ≤ 2 + # bits, # bits0 ≤ (2 + # bits) + # bits2 ⊦ boolvar ↔ boolvar0, lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(2 + # bits + m, bits2 + mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), bits0 = [], boolvar ∧ boolvar0

Rule argument

seq: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1 subst: [bits1, bits0, bits] → [bitsand(boolvar ' + boolvar0 ' + bits, bits0), mklist(boolvar, m), bits2] rotate: F spec: list inst: bitlista name: a

Additional information

Used terms: bitsand(boolvar ' + boolvar0 ' + bits, bits0), mklist(boolvar, m), bits2