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Proof step 64 from proof bxor-flip-one-bit (previous step)

# bits = 1, int2bits(i) = bits + boolvar ', 2 < i, 0 < i, boolvar ∈ int2bits(i) ⊦ i = 0, bits = [], (sgn(bits + (¬ boolvar)')[# int2bits(i) - 1] ↔ ¬ boolvar) ∧ sgn(bits + (¬ boolvar)')[# int2bits(i) - 1, boolvar] = int2bits(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 65:
⊦ # bits = 1 ↔ bits = bits.first + []
Proof step 66:
bits = bits.first + [], int2bits(i) = bits + boolvar ', 2 < i, 0 < i, boolvar ∈ int2bits(i) ⊦ i = 0, bits = [], (sgn(bits + (¬ boolvar)')[# int2bits(i) - 1] ↔ ¬ boolvar) ∧ sgn(bits + (¬ boolvar)')[# int2bits(i) - 1, boolvar] = int2bits(i)

Rule argument

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

Additional information

Used terms: bits