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Proof step 11 from proof cast-max (previous step)

0 < i, 0 < cast(i, j), 1 + (i→n(i) - 1) < # int2bits(cast(i, j)) ⊦ i = 1

User applied rule insert lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < i → # int2bits(cast(i, j)) ≤ i→n(i)

Rule argument

name: cast-length subst: [i, j] → [i, j]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ ¬ n + (m - n) < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: i, j