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Proof step 42 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 ⊦ 2 * 2 ^ i < 4 * 2 ^ i + j ∧ 4 * 2 ^ i + j < 3 * 2 ^ i, 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 43:
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 ⊦ 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(4 * 2 ^ i + j)) - 1), 3 * 2 ^ i + j = 0, ¬ j ≤ ~2 * 2 ^ i ∧ j + 2 ^ i ≠ 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i < ~ j ↔ i + j < 0;% ⊦ i * ~1 = ~ i;% ⊦ (* i2) * i + j < (* i1) * i ↔ j < (i1 - i2) * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;