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Proof step 15 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 = cast(i, j * 2 ^ i + j0) + 2 ^ i

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ 2 ^ i < 0;% ⊦ 0 ≤ i → (i * j < 0 ↔ ¬ ¬(j < 0 ∧ i ≠ 0));% ⊦ i + j < j ↔ i < 0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ 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;% ⊦ ¬ i ≤ j ↔ j < i;