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Proof step 27 from proof bor-2pot-plus-01 (previous step)

0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 0, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i ⊦ bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1)) + mklist(true, i→n(i)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0, i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → sgn(bitsinvert(uint2bits(i)) +1) = int2bits(~ i) subst: [i] → [~ j] rotate: F spec: int2bits inst: name: int2bits-neg-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: ~ j