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Proof step 16 from proof uint2bits-succ (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: (¬ boolvar) ∈ bits ⊦ sgn(boolvar ' + bits + boolvar0 ') = sgn(boolvar ' + bits) + boolvar0 ' subst: [boolvar0, bits, boolvar] → [false, uint2bits(i) +1, false] rotate: F spec: bitopsaux inst: name: sgn-last

Additional information

Used simplifier rules: ⊦ ¬ (¬ boolvar) ∈ bits → sgn(boolvar ' + bits + bits0) = sgn(boolvar ' + bits0);% ⊦ sgn(false ' + false ') = false ';% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits = bits0 + bits ↔ bits0 = [];% ⊦ sgn(boolvar ' + bits) ≠ [];% ⊦ ¬ true ∈ bits +1 ↔ false; Used terms: false, uint2bits(i) +1, false