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Proof step 10 from proof int2bytes-len-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < i ∧ 0 ≤ j → (i < 2 ^ j ↔ # int2bits(i) ≤ i→n(j) + 1)
Proof step 12:
0 < j ∧ 0 ≤ 8 * (i + 1) - 1, # int2bits(j) % 8 = 0, 0 < j, i→n(8 * i) + 1 < # int2bits(j), 0 ≤ i, # int2bits(j) ≤ i→n(8 * (i + 1) - 1) + 1, 8 * i + 1 < 8 * (i + 1) ⊦ # int2bits(j) / 8 = i→n(i) + 1

Rule argument

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

Additional information

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