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Proof step 4 from proof cast-mult-2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < i, j * 2 ^ i < 0 ⊦ cast(i, j * 2 ^ i) = 0

Rule argument

Additional information

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