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Proof step 26 from proof bxor-flip-one-bit (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ bits ≠ [] → (0 ≤ bits2int(bits) ↔ ¬ bits.first)
Proof step 28:
¬ bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))) ≠ [], # int2bits(i) = i→n(j), 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j ⊦ ¬ 0 ≤ bits2int(bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j)))) ∧ int2bits(bits2int(bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j)))))[0, false] = int2bits(i)
Proof step 31:
bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))) ≠ [], # int2bits(i) = i→n(j), 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j ⊦ ¬ ¬ bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))).first ∧ int2bits(bits2int(bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j)))))[0, false] = int2bits(i)

Rule argument

seq: ⊦ bits ≠ [] → (0 ≤ bits2int(bits) ↔ ¬ bits.first) subst: [bits] → [bitsxor (int2bits(i), false ' + true ' + mklist(false, i→n(j)))] rotate: F spec: int2bits inst: name: bits2int-ge-zero

Additional information

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