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Proof step 62 from proof int2bytes-len-ls-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

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