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Proof step 84 from proof bxor-flip-one-bit (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
⊦ (bits.first ↔ ¬ bits.rest.first) ∧ 1 < # bits → sgn(bits) = bits
Proof step 86:
¬(((bits + (¬ boolvar)').first ↔ ¬ (bits + (¬ boolvar)').rest.first) ∧ 1 < #(bits + (¬ boolvar)')), int2bits(i) = bits + boolvar ', 2 < i, 0 < i ⊦ # bits = 1, i = 0, bits = [], (sgn(bits + (¬ boolvar)')[# bits] ↔ ¬ boolvar) ∧ sgn(bits + (¬ boolvar)')[# bits, boolvar] = int2bits(i)
Proof step 98:
((bits + (¬ boolvar)').first ↔ ¬ (bits + (¬ boolvar)').rest.first) ∧ 1 < #(bits + (¬ boolvar)'), int2bits(i) = bits + boolvar ', 2 < i, 0 < i ⊦ # bits = 1, i = 0, bits = [], ((bits + (¬ boolvar)')[# bits] ↔ ¬ boolvar) ∧ (bits + (¬ boolvar)')[# bits, boolvar] = int2bits(i)

Rule argument

seq: ⊦ (bits.first ↔ ¬ bits.rest.first) ∧ 1 < # bits → sgn(bits) = bits subst: [bits] → [bits + (¬ boolvar)'] rotate: F spec: bitopsaux inst: name: sgn-base-05

Additional information

Used terms: bits + (¬ boolvar)'