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Proof step 9 from proof cast-law-mult-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
0 ≤ j, 2 ^ (i - 1) - 1 < j % 2 ^ i, 0 < i ⊦ cast(i, j) = j % 2 ^ i - 2 ^ i
Proof step 11:
¬(0 ≤ j1 ∧ 2 ^ (i - 1) - 1 < j1 % 2 ^ i ∧ 0 < i), 0 < i, 0 ≤ j1, 0 < j1, j1 < 2 ^ i, 0 ≤ i, 0 ≤ i0, 0 < i ⊦ cast(i, j1 * j0) = cast(i, cast(i, j1) * j0)
Proof step 16:
0 ≤ j1 ∧ 2 ^ (i - 1) - 1 < j1 % 2 ^ i ∧ 0 < i, 0 < i, 0 ≤ j1, 0 < j1, j1 < 2 ^ i, 0 ≤ i, 0 ≤ i0, 0 < i ⊦ cast(i, j1 * j0) = cast(i, (j1 % 2 ^ i - 2 ^ i) * j0)

Rule argument

name: cast-mod-pos-high rotate: F subst: [j, i] → [j1, i]

Additional information

Used terms: j1, i