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Proof step 3 from proof cast-law-comm (previous step)

¬(0 < i ∧ 0 < i0 ∧ i < i0), 0 < i, 0 < i0 ⊦ cast(i, cast(i0, j)) = cast(i0, cast(i, j))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
i0 ≤ i, 0 < i0, 0 < i ⊦ cast(i, cast(i0, j)) = cast(i0, cast(i, j))

Rule argument

Additional information

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