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Proof step 89 from proof bxor-flip-one-bit (previous step)

bits.rest + (¬ boolvar)' = boolvar0 ' + bits0, int2bits(i) = bits + boolvar ', 0 < i, 2 < i ⊦ bits.first ↔ ¬ boolvar0, bits = [], i = 0, # bits = 1, (sgn(bits + (¬ boolvar)')[# bits] ↔ ¬ boolvar) ∧ sgn(bits + (¬ boolvar)')[# bits, boolvar] = int2bits(i), ¬(¬ boolvar ↔ boolvar0) ∧ ¬ (¬ boolvar) ∈ bits0, ¬ boolvar0 ∈ bits.rest ∧ ¬(boolvar0 ↔ ¬ boolvar)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 90:
bits = boolvar1 + bits1, bits1 + (¬ boolvar)' = boolvar0 ' + bits0, int2bits(i) = bits + boolvar ', 0 < i, 2 < i ⊦ boolvar1 ↔ ¬ boolvar0, bits = [], i = 0, # bits = 1, (sgn(bits + (¬ boolvar)')[# bits] ↔ ¬ boolvar) ∧ sgn(bits + (¬ boolvar)')[# bits, boolvar] = int2bits(i), ¬(¬ boolvar ↔ boolvar0) ∧ ¬ (¬ boolvar) ∈ bits0, ¬ boolvar0 ∈ bits1 ∧ ¬(boolvar0 ↔ ¬ boolvar)

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [bits, boolvar1, bits1] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

Used simplifier rules: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0); (elim) Used terms: bits, boolvar1, bits1