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Proof step 2 from proof int2bytes-len-le-01 (previous step)

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

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

Rule argument

name: int2bytes-len-ls-01 subst: [i, n] → [i, n -1]

Additional information

Used terms: i, n -1