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Proof step 2 from proof cast-nls-01 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

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

Rule argument

name: cast-max subst: [i, j] → [i, j]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i, j