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Proof step 1 from proof cast-mod-in (conclusion)

0 < i, ~(2 ^ (i - 1)) ≤ j, j < 2 ^ (i - 1) ⊦ cast(i, j) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

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