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Proof step 8 from proof band-011x-is-unsigned (previous step)

0 ≤ i, 0 < i, j < 0, 0 ≤ j + 2 ^ (i - 1) ⊦ (j + 1) % 2 ^ i + 2 ^ i = bits2uint(fillsgn(i→n(i), int2bits(j))) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [2 ^ i, j + 1] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ⊦ i < 0 → abs(i + 1) = abs(i) - 1;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i - j = ~(i + j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0);% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i + j < j ↔ i < 0; Used terms: 2 ^ i, j + 1