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Proof step 34 from proof int2bytes-len-ls-01 (previous step)

# int2bits(i) / 8 = i→n(i0), i < 2 ^ (8 * i0), 2 ^ (8 * i0 - 1) ≤ i, 0 < i, 0 < i0 ⊦ i0 = 0, n ≤ i→n(i0) ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1), i = 0, # int2bits(i) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ 0 < i ∧ 0 ≤ j → (2 ^ j ≤ i ↔ ¬ # int2bits(i) ≤ i→n(j) + 1)
Proof step 36:
0 < i ∧ 0 ≤ 8 * i0 - 1, # int2bits(i) / 8 = i→n(i0), i < 2 ^ (8 * i0), ¬ # int2bits(i) ≤ i→n(8 * i0 - 1) + 1, 0 < i, 0 < i0 ⊦ i0 = 0, n ≤ i→n(i0) ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1), i = 0, # int2bits(i) % 8 = 0

Rule argument

seq: ⊦ 0 < i ∧ 0 ≤ j → (2 ^ j ≤ i ↔ ¬ # int2bits(i) ≤ i→n(j) + 1) subst: [i, j] → [i, 8 * i0 - 1] rotate: F spec: int2bits inst: name: int2bits-lelen-01

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i, 8 * i0 - 1