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Proof step 11 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, cast(i, j1) * j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
0 ≤ i0, j1 % 2 ^ i < 2 ^ (i - 1), 0 ≤ j1, 0 < j1, j1 < 2 ^ i, 0 < i ⊦ cast(i, j1 * j0) = cast(i, cast(i, j1) * j0), 0 = i

Rule argument

Additional information

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