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Proof step 13 from proof int2bits-2pot-04 (previous step)

j < 2 ^ i, 0 < 2 ^ i, 0 ≤ i, j * 2 ^ i < i, j < i, j + 1 < 2 ^ i, j < 0 ⊦ j = 0, sgn((bitsinvert(uint2bits(~ j)) + mklist(true, i→n(i)))+1) = int2bits(j) + mklist(false, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ¬ false ∈ bits0 → (bits + bits0)+1 = bits +1 + bitsinvert(bits0)
Proof step 15:
¬ false ∈ mklist(true, i→n(i)), j < 2 ^ i, 0 < 2 ^ i, 0 ≤ i, j * 2 ^ i < i, j < i, j + 1 < 2 ^ i, j < 0 ⊦ j = 0, sgn(bitsinvert(uint2bits(~ j)) +1 + bitsinvert(mklist(true, i→n(i)))) = int2bits(j) + mklist(false, i→n(i))

Rule argument

seq: ⊦ ¬ false ∈ bits0 → (bits + bits0)+1 = bits +1 + bitsinvert(bits0) subst: [bits0, bits] → [mklist(true, i→n(i)), bitsinvert(uint2bits(~ j))] rotate: F spec: bitopsaux inst: name: succ-zeros-01

Additional information

Used simplifier rules: ⊦ false ∈ bits0 → (bits + bits0)+1 = bits + bits0 +1;% ⊦ mklist(true, n) +1 = true ' + mklist(false, n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ false ∈ mklist(true, n); Used terms: mklist(true, i→n(i)), bitsinvert(uint2bits(~ j))