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Proof step 18 from proof cast-law-add-pos-01 (previous step)

0 ≤ i, 0 ≤ i0, 0 ≤ j1, j1 < 2 ^ i, 2 ^ (i - 1) ≤ j1, 0 < i, j0 < 0 ⊦ cast(i, (i0 * 2 ^ i + j1) + j0) = cast(i, j0 + j1 - 2 ^ i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ 0 < i → cast(i, j * 2 ^ i + j0) = cast(i, j0)
Proof step 20:
0 < i, 0 ≤ i, 0 ≤ i0, 0 ≤ j1, j1 < 2 ^ i, 2 ^ (i - 1) ≤ j1, 0 < i, j0 < 0 ⊦ cast(i, j0 + j1) = cast(i, j0 + j1 - 2 ^ i)

Rule argument

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

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j0 + j1, i0, i