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Proof step 47 from proof int2int-neg (previous step)

j ≤ 4 * 2 ^ i, j < 4 * 2 ^ i, j < 3 * 2 ^ i, j ≤ 3 * 2 ^ i, 2 ^ i + j ≤ 0, 0 < 2 ^ i * 2 + j, 2 ^ i + j ≤ i + 2, 2 ^ i + j < i + 2, j < i + 2, j < 0, j < 2 ^ i, j + 1 < 2 ^ i, j ≤ i, 0 ≤ i, j + 1 < 4 * 2 ^ i, 0 ≤ 4 * 2 ^ i + j, 0 < 4 * 2 ^ i + j, 2 ^ i + j ≤ i, j < i, j ≤ i + 2, j ≤ 0, j ≤ 2 ^ i, 0 ≤ 2 ^ i, 0 < 2 ^ i ⊦ j + 2 ^ i ≠ 0, 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(4 * 2 ^ i + j)) - 1), 3 * 2 ^ i + j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
j + 2 ^ i = 0, j < 0, j < i + 2, j ≤ 0, j ≤ i + 2, j ≤ 4 * 2 ^ i, j < 4 * 2 ^ i, j < 3 * 2 ^ i, j ≤ 3 * 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j ≤ i, j + 1 < 4 * 2 ^ i, j < i, j ≤ 2 ^ i, 0 < 2 ^ i * 2 + j, 0 < 4 * 2 ^ i + j, 0 < 2 ^ i, ~2 ≤ i, 0 ≤ 4 * 2 ^ i + j, 0 ≤ i, 0 ≤ 2 ^ i, ~2 < i ⊦ 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(4 * 2 ^ i + j)) - 1), 3 * 2 ^ i + j = 0

Rule argument

Additional information

Used simplifier rules: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i + (* j) < i0 + (* j0) ↔ i < i0 + (j0 - j);% ⊦ i +1 = i + 1;% ⊦ i < i + j ↔ 0 < j;% ⊦ 0 ≤ i ∧ i ≤ 1 → i = 0 ∨ i = 1; (forward)% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;