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Proof step 2 from proof cast-mult-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
0 ≤ j, 2 ^ (i - 1) - 1 < j % 2 ^ i, 0 < i ⊦ cast(i, j) = j % 2 ^ i - 2 ^ i
Proof step 4:
¬(0 ≤ j0 ∧ 2 ^ (i - 1) - 1 < j0 % 2 ^ i ∧ 0 < i), 0 ≤ j, 0 ≤ j0, 0 < i ⊦ cast(i, j * 2 ^ i + j0) = cast(i, j0)
Proof step 12:
0 ≤ j0 ∧ 2 ^ (i - 1) - 1 < j0 % 2 ^ i ∧ 0 < i, 0 ≤ j, 0 ≤ j0, 0 < i ⊦ cast(i, j * 2 ^ i + j0) = j0 % 2 ^ i - 2 ^ i

Rule argument

name: cast-mod-pos-high rotate: F subst: [j, i] → [j0, i]

Additional information

Used terms: j0, i