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Proof step 2 from proof cast-nls (previous step)

cast(i, j) < j0, 0 < i, j0 + 2 ^ (i - 1) ≤ 0, j0 + 2 ^ (i - 1) < i ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i → ~(2 ^ (i - 1)) ≤ cast(i, j)

Rule argument

name: cast-min subst: [i, j] → [i, j]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i + j ≤ i0 + j ↔ i ≤ i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i, j