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Proof step 40 from proof int2bytes-len-ls-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ 0 < i ∧ 0 ≤ j → (i < 2 ^ j ↔ # int2bits(i) ≤ i→n(j) + 1)
Proof step 42:
0 < i ∧ 0 ≤ 8 * i0, # int2bits(i) / 8 = i→n(i0), i→n(8 * i0 - 1) + 1 < # int2bits(i), 0 < i, # int2bits(i) ≤ i→n(8 * i0) + 1, 0 < i0 ⊦ # int2bits(i) % 8 = 0, i = 0, n→i(n) ≤ i0 ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1), i0 = 0

Rule argument

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

Additional information

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