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Proof step 10 from proof int2bytes-len-neg-01 (previous step)

# int2bits(j) = n0 * 8, n * 8 = n0 * 8, j + 2 ^ (8 * (i + 1) - 1) < 0, 0 < j + 2 ^ (8 * (i + 1)), 0 ≤ i ⊦ n0 = i→n(i + 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ j < 0 ∧ 1 < n → (# int2bits(j) = n ↔ ~(2 ^ (n→i(n) - 1)) ≤ j ∧ j < ~(2 ^ (n→i(n) - 2)))
Proof step 12:
j < 0 ∧ 1 < n0 * 8, ~(2 ^ (n→i(n0 * 8) - 1)) ≤ j ∧ j < ~(2 ^ (n→i(n0 * 8) - 2)), n * 8 = n0 * 8, j + 2 ^ (8 * (i + 1) - 1) < 0, 0 < j + 2 ^ (8 * (i + 1)), 0 ≤ i ⊦ n0 = i→n(i + 2)

Rule argument

seq: ⊦ j < 0 ∧ 1 < n → ( # int2bits(j) = n ↔ ~(2 ^ (n→i(n) - 1)) ≤ j ∧ j < ~(2 ^ (n→i(n) - 2))) subst: [n, j] → [n0 * 8, j] rotate: F spec: int2bits inst: name: int2bits-leneq-neg

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);%0 ≠ m ⊦ (* m) * n = 0 ↔ n = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ m0 * m = 1 ↔ m0 = 1 ∧ m = 1;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i + j < j ↔ i < 0;% ⊦ ¬ 2 ^ i < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: n0 * 8, j