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Proof step 33 from proof int2bytes-first-zerobyte-01 (previous step)

2 ^ (j0 + 8 * i0 - 2) < 2 ^ (j0 + 8 * i0 - 1), j < 2 ^ (j0 + 8 * i0 - 1), 2 ^ (j0 + 8 * i0 - 2) ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ j, j0 < 8, 0 < j0 + 8 * i0 ⊦ 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), i0 = 0 ∧ j0 = 1

User applied rule cut formula

And obtained the following new goals

Proof step 34:
i0 = 0, 2 ^ (j0 + 8 * i0 - 2) < 2 ^ (j0 + 8 * i0 - 1), j < 2 ^ (j0 + 8 * i0 - 1), 2 ^ (j0 + 8 * i0 - 2) ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ j, j0 < 8, 0 < j0 + 8 * i0 ⊦ 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), i0 = 0 ∧ j0 = 1
Proof step 40:
2 ^ (j0 + 8 * i0 - 2) < 2 ^ (j0 + 8 * i0 - 1), j < 2 ^ (j0 + 8 * i0 - 1), 2 ^ (j0 + 8 * i0 - 2) ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ j, j0 < 8, 0 < j0 + 8 * 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), i0 = 0 ∧ j0 = 1

Rule argument

fma: i0 = 0

Additional information

Used formulas: i0 = 0