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Proof step 16 from proof cast-law-mult-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
0 ≤ j1, 0 < j1, j1 < 2 ^ i, 0 ≤ i, 0 ≤ i0, 0 < i, 2 ^ (i - 1) ≤ j1 % 2 ^ i ⊦ cast(i, j1 * j0) = cast(i, (j1 % 2 ^ i - 2 ^ i) * j0)

Rule argument

Additional information

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