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Proof step 11 from proof int2bytes-len-pos-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 0 ≤ j ∧ 1 < n → (# int2bits(j) = n ↔ 2 ^ (n→i(n) - 2) ≤ j ∧ j < 2 ^ (n→i(n) - 1))
Proof step 13:
0 ≤ j ∧ 1 < m * 8, 2 ^ (n→i(m * 8) - 2) ≤ j ∧ j < 2 ^ (n→i(m * 8) - 1), 0 ≤ i, j < 2 ^ (8 * (i + 1)), 2 ^ (8 * (i + 1) - 1) ≤ j ⊦ m = i→n(i + 2)

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] → [m * 8, j] rotate: F spec: int2bits inst: name: int2bits-leneq-pos

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 ∧ j ≤ j0 → i < j0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ 2 ^ i < 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: m * 8, j