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Proof step 18 from proof cast-if (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
0 < i ⊦ ~(2 ^ (i - 1)) ≤ j ∧ j < 2 ^ (i - 1) → cast(i, j) = j
Proof step 20:
¬(0 < i ∧ ~(2 ^ (i - 1)) ≤ j ∧ j < 2 ^ (i - 1)), 0 ≤ j ∨ 2 ^ (i - 1) + j % 2 ^ i < 0, 0 ≤ j ∨ 0 ≤ j % 2 ^ i + 2 ^ (i - 1), j < 0 ∨ j % 2 ^ i < 2 ^ (i - 1), j < 0 ∨ 2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i ⊦ cast(i, j) = j

Rule argument

name: cast-size-fits-01 rotate: F subst: [j, i] → [j, i]

Additional information

Used terms: j, i