[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 111 from proof bxor-flip-one-bit (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 112:
⊦ # bits = 1 ↔ bits = bits.first + []
Proof step 113:
bits0 = bits0.first + [], # bits = i→n(j), int2bits(i) = bits0 + bits, bitsxor(bits0 + bits, (false ' + true ') + mklist(false, i→n(j))) = bitsxor(bits0, false ' + true ') + bitsxor(bits, mklist(false, i→n(j))), 0 ≤ j, 0 ≤ i, 2 ^ j * 2 < i ⊦ bits = [], bits0 = [], bitsxor(bits0, false ' + true ') + bitsxor(bits, mklist(false, i→n(j))) = [], (sgn(bitsxor(bits0, false ' + true ') + bitsxor(bits, mklist(false, i→n(j))))[0] ↔ ¬ bits0.last) ∧ sgn(bitsxor(bits0, false ' + true ') + bitsxor(bits, mklist(false, i→n(j))))[0, bits0.last] = bits0 + bits

Rule argument

seq: ⊦ # bits = 1 ↔ bits = bits.first + [] subst: [bits] → [bits0] rotate: F spec: list-data inst: bitlista name: lf-01

Additional information

Used terms: bits0