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Proof step 4 from proof cast-law-add-pos-01 (previous step)

¬(0 ≤ j ∧ 0 ≤ j0 ∧ 0 < i), 0 ≤ j, 0 < i ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j0 < 0, 0 < i, 0 ≤ j ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0)

Rule argument

Additional information

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