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Proof step 12 from proof cast-if (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
j < 0, j % 2 ^ i < ~(2 ^ (i - 1)), 0 < i ⊦ cast(i, j) = j % 2 ^ i + 2 ^ i

Rule argument

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

Additional information

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