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Proof step 7 from proof cast-mult-add-h-01 (previous step)

0 < j, 0 ≤ j0 + 2 ^ i, 0 < i, 0 ≤ j, j0 < 0, 0 < 2 ^ i + j0 ⊦ cast(i, j0 + 2 ^ i) = cast(i, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ~(2 ^ i) < j ∧ j < 0 ∧ 0 < i → cast(i, j + 2 ^ i) = cast(i, j)

Rule argument

name: cast-add-2pot-h rotate: F subst: [j, i] → [j0, i]

Additional information

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