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Proof step 5 from proof cast-law-neg (previous step)

j % 2 ^ i < 0, 0 < i, j < 0 ⊦ cast(i, ~ j) = cast(i, ~ cast(i, j))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
j = i0 * 2 ^ i + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 2 ^ i ∧ i0 ≤ 0 ∧ 0 < 2 ^ i, j0 < 0, 0 < i, j < 0 ⊦ cast(i, ~ j) = cast(i, ~ cast(i, j))

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0) subst: [i, j, i0, j0] → [j, 2 ^ i, i0, j0] rotate: T spec: int-div inst: name: div-elim-negpos

Additional information

Used simplifier rules: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);%⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0); (elim) Used terms: j, 2 ^ i, i0, j0