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Proof step 3 from proof cast-mod-ls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
j < 2 ^ (i - 1), j < 0, 0 < i, 0 < 2 ^ (i - 1) + j ⊦ cast(i, j) = j

Rule argument

Additional information

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