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Proof step 7 from proof cast-mult-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 ≤ j, 0 ≤ j0, 0 < i, j0 % 2 ^ i < 2 ^ (i - 1) ⊦ cast(i, j * 2 ^ i + j0) = j0 % 2 ^ 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;