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Proof step 161 from proof bxor-flip-one-bit (previous step)

int2bits(i) = (bits1 + boolvar ') + bits, # bits = i→n(j), bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (bits1 + (¬ boolvar)') + bitsxor(bits, mklist(false, i→n(j))), bits1.first ↔ ¬ (bits1.rest + (¬ boolvar)').first, 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j ⊦ bits = [], bits1 = [], (bits1 + (¬ boolvar)')[# bits1, boolvar] + bitsxor(bits, mklist(false, i→n(j))) = int2bits(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 162:
⊦ n = # bits → (bits + boolvar ')[n, boolvar0] = bits + boolvar0 '
Proof step 163:
# bits1 = # bits1, int2bits(i) = (bits1 + boolvar ') + bits, # bits = i→n(j), bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (bits1 + (¬ boolvar)') + bitsxor(bits, mklist(false, i→n(j))), bits1.first ↔ ¬ (bits1.rest + (¬ boolvar)').first, 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j ⊦ bits = [], bits1 = [], (bits1 + boolvar ') + bitsxor(bits, mklist(false, i→n(j))) = int2bits(i)

Rule argument

seq: ⊦ n = # bits → (bits + boolvar ')[n, boolvar0] = bits + boolvar0 ' subst: [boolvar0, n, boolvar, bits] → [boolvar, # bits1, ¬ boolvar, bits1] rotate: F spec: list-del inst: bitlista name: put-last

Additional information

Used terms: boolvar, # bits1, ¬ boolvar, bits1