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Proof step 41 from proof int2bytes-first-zerobyte-01 (previous step)

0 ≤ j0, 0 ≤ j, j0 < 8, 0 < j0 + 8 * i0, 2 ^ (j0 + 8 * i0 - 2) < 2 ^ (j0 + 8 * i0 - 1), j < 2 ^ (j0 + 8 * i0 - 1), 2 ^ (j0 + 8 * i0 - 2) ≤ j, 0 < i0 ⊦ i0 = 0, 8 * i→n(i0) = 1, i→n(j0) + 8 * i→n(i0) = 0, 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 42:
⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0)
Proof step 43:
¬ 0 ≤ j0 + 8 * i0 - 2, 0 ≤ j0, 0 ≤ j, j0 < 8, 0 < j0 + 8 * i0, 2 ^ (j0 + 8 * i0 - 2) < 2 ^ (j0 + 8 * i0 - 1), j < 2 ^ (j0 + 8 * i0 - 1), 2 ^ (j0 + 8 * i0 - 2) ≤ j, 0 < i0 ⊦ i0 = 0, 8 * i→n(i0) = 1, i→n(j0) + 8 * i→n(i0) = 0, j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)
Proof step 46:
0 ≤ j0 + 8 * i0 - 2, 0 ≤ j0, 0 ≤ j, j0 < 8, 0 < j0 + 8 * i0, j0 + 8 * i0 - 2 < j0 + 8 * i0 - 1, j < 2 ^ (j0 + 8 * i0 - 1), 2 ^ (j0 + 8 * i0 - 2) ≤ j, 0 < i0 ⊦ i0 = 0, 8 * i→n(i0) = 1, i→n(j0) + 8 * i→n(i0) = 0, j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)

Rule argument

seq: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0) subst: [j0, j] → [j0 + 8 * i0 - 1, j0 + 8 * i0 - 2] rotate: F spec: int-pot inst: name: ls-pos-2pot

Additional information

Used terms: j0 + 8 * i0 - 1, j0 + 8 * i0 - 2