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Proof step 148 from proof bxor-flip-one-bit (previous step)

bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (false ' + bits0) + (¬ boolvar)' + bitsxor(bits, mklist(false, i→n(j))), # bits = i→n(j), int2bits(i) = (false ' + bits0) + boolvar ' + bits, false ∈ bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))), false ∈ int2bits(i), 3 + i→n(j) ≤ # int2bits(i), 0 ≤ j, 0 < i ⊦ bits = [], i = 2 ^ j * 2, # int2bits(i) = 2 + i→n(j), i = 0, (bits0 + (¬ boolvar)').first, (sgn(bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))))[1 + # bits0] ↔ ¬ boolvar) ∧ sgn(bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))))[1 + # bits0, boolvar] = int2bits(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [(¬ boolvar)', bits0] rotate: F spec: list inst: bitlista name: first-01

Additional information

Used terms: (¬ boolvar)', bits0