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Proof step 38 from proof bxor-flip-one-bit (previous step)

2 ^ (j + 1) < 2 ^ (j - 1), 0 ≤ j, 0 ≤ i, 2 ^ (j + 1) < i, i < 2 ^ (j - 1), 2 ^ (j - 2) ≤ i, 0 < j ⊦ j = 0, j = 1, bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))) = [], bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))).first ∧ sgn(bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))))[0, false] = int2bits(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0) subst: [j0, j] → [j - 1, j + 1] rotate: F spec: int-pot inst: name: ls-pos-2pot

Additional information

Used simplifier rules: ⊦ i + j < j ↔ i < 0;% ⊦ i < j - i0 ↔ i + i0 < j;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i;% ⊦ i + j = j + i; Used terms: j - 1, j + 1