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Proof step 2 from proof int2bytes-len-ls (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i ∧ int2bytes(i).first ≠ i2b(0) → (n ≤ # int2bytes(i) ↔ 2 ^ ((n→i(n) - 1) * 8) ≤ i)
Proof step 4:
0 ≤ i ∧ int2bytes(i).first ≠ i2b(0) → (n + 1 ≤ # int2bytes(i) ↔ 2 ^ ((n→i(n + 1) - 1) * 8) ≤ i), 0 ≤ i ⊦ int2bytes(i).first = i2b(0), n < # int2bytes(i) ↔ ¬ i < 2 ^ (n→i(n) * 8)

Rule argument

name: int2bytes-len-le subst: [i, n] → [i, n + 1]

Additional information

Used terms: i, n + 1