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Proof step 91 from proof int2bytes-len-ls-01 (previous step)

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

Additional information

Used simplifier rules: 0 ≠ m ⊦ (* m) * n = 0 ↔ n = 0;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1;% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ n→i(m * n) = n→i(m) * n→i(n);% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i + 0 = i;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < n ↔ n ≠ 0;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0);% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i→n(i0) * 8 + 1, i