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Proof step 14 from proof cast-law-mult-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 ≤ i0, 0 ≤ j1, 0 < j1, j1 < 2 ^ i, 0 < i, j1 % 2 ^ i < 2 ^ (i - 1) ⊦ cast(i, j1 * j0) = cast(i, j1 % 2 ^ i * j0), 0 = i

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;