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Proof step 4 from proof int2bytes-len-ls-neg (previous step)

i < 0 ⊦ int2bytes(i).first = i2b(~1), ¬ # int2bytes(i) ≤ n ↔ ¬ 0 ≤ i + 2 ^ (8 * n→i(n))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i < 0 ∧ int2bytes(i).first ≠ i2b(~1) → (# int2bytes(i) ≤ n ↔ ~(2 ^ (8 * n→i(n))) ≤ i)

Rule argument

name: int2bytes-len-le-neg-02 rotate: F subst: [n, i] → [n, i]

Additional information

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