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Proof step 18 from proof int2bytes-first-zerobyte-01 (previous step)

# int2bits(j) = i→n(j0) + 8 * i→n(i0), j0 < 8, 0 ≤ j, 0 ≤ j0, 0 ≤ i0 ⊦ j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ 0 ≤ j ∧ 1 < n → (# int2bits(j) = n ↔ 2 ^ (n→i(n) - 2) ≤ j ∧ j < 2 ^ (n→i(n) - 1))
Proof step 20:
¬(0 ≤ j ∧ 1 < i→n(j0) + 8 * i→n(i0)), # int2bits(j) = i→n(j0) + 8 * i→n(i0), j0 < 8, 0 ≤ j, 0 ≤ j0, 0 ≤ i0 ⊦ j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)
Proof step 32:
0 ≤ j ∧ 1 < i→n(j0) + 8 * i→n(i0), 2 ^ (n→i(i→n(j0) + 8 * i→n(i0)) - 2) ≤ j ∧ j < 2 ^ (n→i(i→n(j0) + 8 * i→n(i0)) - 1), j0 < 8, 0 ≤ j, 0 ≤ j0, 0 ≤ i0 ⊦ j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)

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(j0) + 8 * i→n(i0), j] rotate: F spec: int2bits inst: name: int2bits-leneq-pos

Additional information

Used terms: i→n(j0) + 8 * i→n(i0), j