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Proof step 4 from proof cast-mult-add-h-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ j ∧ 0 ≤ j0 ∧ 0 < i → cast(i, j * 2 ^ i + j0) = cast(i, j0)
Proof step 6:
0 ≤ j - 1 ∧ 0 ≤ j0 + 2 ^ i ∧ 0 < i, 0 < 2 ^ i + j0, j0 < 0, 0 ≤ j, 0 < i ⊦ cast(i, j0 + 2 ^ i) = cast(i, j0)

Rule argument

name: cast-mult-pos rotate: F subst: [j0, j, i] → [j0 + 2 ^ i, j - 1, i]

Additional information

Used simplifier rules: ⊦ i * j + i = i * (j + 1);% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i * 0 = 0;% ⊦ i + 0 = i; Used terms: j0 + 2 ^ i, j - 1, i