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Proof step 47 from proof int2bytes-first-zerobyte-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 48:
j0 = 1, 2 ≤ j0 + 8 * i0, 2 ^ (j0 + 8 * i0 - 2) ≤ j, j < 2 ^ (j0 + 8 * i0 - 1), 0 < j0 + 8 * i0, j0 < 8, 0 ≤ j, 0 ≤ j0, 0 < i0 ⊦ j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j), i→n(j0) + 8 * i→n(i0) = 0, 8 * i→n(i0) = 1, i0 = 0
Proof step 50:
2 ≤ j0 + 8 * i0, 2 ^ (j0 + 8 * i0 - 2) ≤ j, j < 2 ^ (j0 + 8 * i0 - 1), 0 < j0 + 8 * i0, j0 < 8, 0 ≤ j, 0 ≤ j0, 0 < i0 ⊦ j0 = 1, j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j), i→n(j0) + 8 * i→n(i0) = 0, 8 * i→n(i0) = 1, i0 = 0

Rule argument

fma: j0 = 1

Additional information

Used formulas: j0 = 1