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Proof step 5 from proof cast-mult-2pot (previous step)

0 < i, j * 2 ^ i < 0 ⊦ cast(i, j * 2 ^ i) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
j < 0, ~(2 ^ (i - 1)) ≤ j % 2 ^ i, 0 < i ⊦ cast(i, j) = j % 2 ^ i

Rule argument

name: cast-mod-neg-high rotate: F subst: [j, i] → [j * 2 ^ i, i]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);%j ≠ 0 ⊦ (i * j) % j = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ 2 ^ i < 0; Used terms: j * 2 ^ i, i