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

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

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
Proof step 7:
j < 0 ∧ ~(2 ^ (i - 1)) ≤ j % 2 ^ i ∧ 0 < i, 0 ≤ j % 2 ^ i + 2 ^ (i - 1), 0 < j + 2 ^ i, 0 < i, j < 0 ⊦ cast(i, j + 2 ^ i) = j % 2 ^ i

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = j + i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: j, i