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

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ j ∧ 0 ≤ j0 ∧ 0 < i → (j * 2 ^ i + j0) % 2 ^ i = j0 % 2 ^ i;