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Proof step 47 from proof bxor-flip-one-bit (previous step)

# bits = i→n(j), int2bits(i) = bits0 + bits, 0 ≤ j, 0 ≤ i, 2 ^ j * 2 < i ⊦ bits0 = [], (int2bits(bits2int(bitsxor(bits0 + bits, false ' + true ' + mklist(false, i→n(j)))))[# bits0 - 1] ↔ ¬ bits0.last) ∧ int2bits(bits2int(bitsxor(bits0 + bits, false ' + true ' + mklist(false, i→n(j)))))[# bits0 - 1, bits0.last] = bits0 + bits

User applied rule insert lemma

And obtained the following new goals

Proof step 48:
⊦ # bits0 = # bits2 ∧ bits ≠ [] ∧ bits0 ≠ [] ∧ bits1 ≠ [] → bitsxor(bits + bits0, bits1 + bits2) = bitsxor(bits, bits1) + bitsxor(bits0, bits2)
Proof step 49:
# bits = # mklist(false, i→n(j)) ∧ bits0 ≠ [] ∧ bits ≠ [] ∧ false ' + true ' ≠ [] → bitsxor(bits0 + bits, (false ' + true ') + mklist(false, i→n(j))) = bitsxor(bits0, false ' + true ') + bitsxor(bits, mklist(false, i→n(j))), # bits = i→n(j), int2bits(i) = bits0 + bits, 0 ≤ j, 0 ≤ i, 2 ^ j * 2 < i ⊦ bits0 = [], (int2bits(bits2int(bitsxor(bits0 + bits, false ' + true ' + mklist(false, i→n(j)))))[# bits0 - 1] ↔ ¬ bits0.last) ∧ int2bits(bits2int(bitsxor(bits0 + bits, false ' + true ' + mklist(false, i→n(j)))))[# bits0 - 1, bits0.last] = bits0 + bits

Rule argument

name: bitsxor-append-same-size subst: [bits0, bits2, bits, bits1] → [bits, mklist(false, i→n(j)), bits0, false ' + true ']

Additional information

Used terms: bits, mklist(false, i→n(j)), bits0, false ' + true '