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Proof step 14 from proof cast-mult-add (previous step)

0 ≤ i0 + j, i0 < 0, 0 < i, i0 * 2 ^ i + j1 < 0, j1 < 0, 0 < 2 ^ i + j1, i0 < 2 ^ i + j1, 0 ≤ i ⊦ cast(i, 2 ^ i * (i0 + j) + j1) = cast(i, j1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ 0 ≤ j ∧ j0 < 0 ∧ abs(j0) < 2 ^ i ∧ 0 < i → cast(i, j * 2 ^ i + j0) = cast(i, j0)

Rule argument

name: cast-mult-add-h-01 rotate: F subst: [j0, j, i] → [j1, i0 + j, i]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: j1, i0 + j, i