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Proof step 116 from proof bxor-flip-one-bit (previous step)

# bits = i→n(j), bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (false ' + true ') + bitsxor(bits, mklist(false, i→n(j))), int2bits(i) = false ' + bits, 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j, false ∈ int2bits(i) ⊦ bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 117:
⊦ # bits = # bits0 ∧ 1 < # bits → bitsxor(bits, bits0) = (¬(bits.first ↔ bits0.first))' + bitsxor(bits.rest, bits0.rest)
Proof step 118:
¬(# int2bits(i) = #((false ' + true ') + mklist(false, i→n(j))) ∧ 1 < # int2bits(i)), # bits = i→n(j), bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (false ' + true ') + bitsxor(bits, mklist(false, i→n(j))), int2bits(i) = false ' + bits, 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j, false ∈ int2bits(i) ⊦ bits = []
Proof step 125:
# int2bits(i) = #((false ' + true ') + mklist(false, i→n(j))) ∧ 1 < # int2bits(i), # bits = i→n(j), (¬(int2bits(i).first ↔ ((false ' + true ') + mklist(false, i→n(j))).first))' + bitsxor(int2bits(i).rest, ((false ' + true ') + mklist(false, i→n(j))).rest) = (false ' + true ') + bitsxor(bits, mklist(false, i→n(j))), int2bits(i) = false ' + bits, 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j, false ∈ int2bits(i) ⊦ bits = []

Rule argument

name: bitsxor-first rotate: F subst: [bits0, bits] → [(false ' + true ') + mklist(false, i→n(j)), int2bits(i)]

Additional information

Used terms: (false ' + true ') + mklist(false, i→n(j)), int2bits(i)