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Proof step 15 from proof uint2bits-pred (previous step)

0 < i, ∀ j0. i→n(j0) < i→n(i * 2 + 0) → 0 < j0 → uint2bits(j0 - 1) = sgn(bitsinvert(bitsinvert(uint2bits(j0)) +1)) ⊦ i = 1, sgn(bitsinvert(bitsinvert(uint2bits(i)) +1)) + true ' = sgn(bitsinvert(bitsinvert(uint2bits(i)) +1) + true ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
(¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar '

Rule argument

seq: (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar ' subst: [boolvar, bits] → [true, bitsinvert(bitsinvert(uint2bits(i)) +1)] rotate: F spec: bitopsaux inst: name: sgn-last-diff

Additional information

Used simplifier rules: ⊦ false ∈ bitsinvert(bits) ↔ true ∈ bits;% ⊦ ¬ true ∈ bits +1 ↔ false; Used terms: true, bitsinvert(bitsinvert(uint2bits(i)) +1)