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Proof step 21 from proof cast-if (previous step)

0 < i, 0 ≤ j ∨ 2 ^ (i - 1) + j % 2 ^ i < 0, 0 ≤ j ∨ 0 ≤ j % 2 ^ i + 2 ^ (i - 1), j < 0 ∨ j % 2 ^ i < 2 ^ (i - 1), j < 0 ∨ 2 ^ (i - 1) ≤ j % 2 ^ i ⊦ cast(i, j) = j, ¬ 2 ^ (i - 1) + j < 0 ∧ ¬ 2 ^ (i - 1) ≤ j

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 2

Additional information

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