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Proof step 130 from proof bxor-flip-one-bit (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 131:
bits0 = bits1 + boolvar ', int2bits(i) = bits0 + bits, # bits = i→n(j), bitsxor(bits0 + bits, (false ' + true ') + mklist(false, i→n(j))) = (bitsxor(bits1, false ') + (¬ boolvar)') + bitsxor(bits, mklist(false, i→n(j))), 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j ⊦ bits0 = [], bits = [], # bits0 = 1, (sgn(bitsxor(bits0 + bits, (false ' + true ') + mklist(false, i→n(j))))[# bits0 - 1] ↔ ¬ boolvar) ∧ sgn(bitsxor(bits0 + bits, (false ' + true ') + mklist(false, i→n(j))))[# bits0 - 1, boolvar] = bits0 + bits

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits0, boolvar, bits1] rotate: T spec: list-last inst: bitlista name: last-elim

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar '; (elim) Used terms: bits0, boolvar, bits1