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Proof step 3 from proof cast-law-add-one (previous step)

¬(0 ≤ j ∧ 0 ≤ j0 ∧ 0 < i), 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 4:
0 < i ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0), ¬ j < 0 ∧ ¬ j0 < 0

Rule argument

Additional information

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