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Proof step 21 from proof rightshift-8-01-01 (previous step)

0 ≤ i, # int2bytes(i) ≤ i→n(j), 2 ^ (8 * abs(j)) ≤ i ⊦ j = 0, i / 2 ^ (8 * abs(j)) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 0 ≤ i ∧ int2bytes(i).first = i2b(0) → (# int2bytes(i) ≤ n ↔ i < 2 ^ (n→i(n) * 8 - 1))
Proof step 23:
¬(0 ≤ i ∧ int2bytes(i).first = i2b(0)), 0 ≤ i, # int2bytes(i) ≤ i→n(j), 2 ^ (8 * abs(j)) ≤ i ⊦ j = 0, i / 2 ^ (8 * abs(j)) = 0

Rule argument

name: int2bytes-len-le-upper rotate: F subst: [n, i] → [i→n(j), i]

Additional information

Used simplifier rules: ⊦ n→i(i→n(i)) = abs(i);% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 0 < abs(i) ↔ i ≠ 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 ≤ abs(i);% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ (* i2) * i + j < (* i1) * i ↔ j < (i1 - i2) * i;% ⊦ i * 0 = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i→n(j), i