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Proof step 7 from proof cast-law-add-pos-01 (previous step)

¬(0 ≤ j ∧ 2 ^ (i - 1) - 1 < j % 2 ^ i ∧ 0 < i), j0 < 0, 0 < i, 0 ≤ j ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j0 < 0, 0 < i, 0 ≤ j, j % 2 ^ i < 2 ^ (i - 1) ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0)

Rule argument

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;