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Proof step 34 from proof int2bytes-len-le-neg-03 (previous step)

int2bytes(i).first = i2b(~1), n < # int2bytes(i), 2 ≤ # int2bytes(i), 0 ≤ b2i(int2bytes(i).rest.first), 1 ≤ # int2bytes(i), 2 ^ (8 * (n→i(# int2bytes(i)) - 1) - 1) + i < 0, 0 ≤ 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) + i, 0 ≤ 2 ^ (8 * n→i(n) - 1) + i, 2 ^ (8 * (n→i(# int2bytes(i)) - 1) - 1) < 2 ^ (8 * n→i(n) - 1) ⊦ int2bytes(i).rest = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0) subst: [j0, j] → [8 * n→i(n) - 1, 8 * (n→i(# int2bytes(i)) - 1) - 1] rotate: F spec: int-pot inst: name: ls-pos-2pot

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];%int2bytes-empty: ⊦ int2bytes(i) ≠ [];% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)%0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i < j - i0 ↔ i + i0 < j;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ # bytes = 0 ↔ bytes = [];% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n;% ⊦ m < n → (n ≤ m ↔ false); Used terms: 8 * n→i(n) - 1, 8 * (n→i(# int2bytes(i)) - 1) - 1