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Proof step 21 from proof cast-law-add-pos (previous step)

0 ≤ i0 ∧ 0 ≤ j1 + j0 ∧ 0 < i, 0 ≤ i, 0 ≤ i0, 0 ≤ j1, j1 < 2 ^ i, 2 ^ (i - 1) ≤ j1, 0 < i, 0 ≤ j0 ⊦ cast(i, j1 + j0) = cast(i, j0 + j1 - 2 ^ i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
0 ≤ i, 0 ≤ i0, 0 ≤ j1, j1 < 2 ^ i, 2 ^ (i - 1) ≤ j1, 0 < i, 0 ≤ j0, 0 ≤ j1 + j0 ⊦ cast(i, j1 + j0) = cast(i, j0 + j1 - 2 ^ i)

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)