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Proof step 7 from proof int2bits-2pot-04 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i < 0 → int2bits(i) = sgn(bitsinvert(uint2bits(abs(i))) +1)
Proof step 9:
j * 2 ^ i < 0, j < 2 ^ i, 0 < 2 ^ i, 0 ≤ i, j < 0, j * 2 ^ i < i, j < i, j + 1 < 2 ^ i ⊦ sgn(bitsinvert(uint2bits(abs(j * 2 ^ i))) +1) = int2bits(j) + mklist(false, i→n(i)), j = 0

Rule argument

name: int2bits-neg rotate: F subst: [i] → [j * 2 ^ i]

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: j * 2 ^ i