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Proof step 16 from proof cast-law-add-one (previous step)

0 < i, 0 < i, 0 ≤ i, i0 < 2 ^ i + j1, i0 < i, i0 ≤ 0, 0 < 2 ^ i + j1, i0 * 2 ^ i + j1 < 0, j1 < 0, 0 < i ⊦ cast(i, j0 + j1) = cast(i, cast(i, 2 ^ i + j1) + j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 0 ≤ j ∧ 0 < i → cast(i, j + j0) = cast(i, cast(i, j) + j0)

Rule argument

name: cast-law-add-pos-01 rotate: T subst: [j0, j, i] → [j0, 2 ^ i + j1, i]

Additional information

Used simplifier rules: cast-add-2pot: ⊦ 0 < i → cast(i, j + 2 ^ i) = cast(i, j);%cast-add-2pot: ⊦ 0 < i → cast(i, j + 2 ^ i) = cast(i, j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j); Used terms: j0, 2 ^ i + j1, i