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Proof step 10 from proof int2int-lastn-pospos (previous step)

int2bits(i) = lastn(# int2bits(i), int2bits(i)), 0 < i, 2 ^ n→i(# int2bits(i)) ≤ i ⊦ i = i % 2 ^ n→i(# int2bits(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < i ∧ 0 ≤ j → (2 ^ j ≤ i ↔ ¬ # int2bits(i) ≤ i→n(j) + 1)

Rule argument

name: int2bits-lelen-01 rotate: F subst: [i, j] → [i, n→i(# int2bits(i))]

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ n→i(n);% ⊦ i→n(n→i(n)) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: i, n→i(# int2bits(i))