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Proof step 6 from proof intshiftrsign-2pot-neg-02 (previous step)

i = i0 * 2 ^ j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 2 ^ j ∧ i0 ≤ 0 ∧ 0 < 2 ^ j, j < 32, i < 0, 0 < j ⊦ j0 = 0, i0 = 1 + (i + 1 - 2 ^ j) / 2 ^ j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 ≤ j, i0 < 2 ^ j + j0, i0 < j, i0 ≤ 0, 0 < 2 ^ j + j0, j0 < 0, i0 * 2 ^ j + j0 < 0, 0 < j, j < 32 ⊦ i0 = 1 + ((i0 * 2 ^ j + j0) + 1 - 2 ^ j) / 2 ^ j, j0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);