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Proof step 4 from proof square-ex (previous step)

0 ≤ i0, 0 < i0 → 0 < j ∧ j * j ≤ i0 ∧ i0 < (j + 1) * (j + 1) ⊦ ∃ j0. 0 < j0 ∧ j0 * j0 ≤ i0 + 1 ∧ i0 + 1 < (j0 + 1) * (j0 + 1)

User applied rule cut formula

And obtained the following new goals

Proof step 5:
0 < i0, 0 ≤ i0, 0 < i0 → 0 < j ∧ j * j ≤ i0 ∧ i0 < (j + 1) * (j + 1) ⊦ ∃ j0. 0 < j0 ∧ j0 * j0 ≤ i0 + 1 ∧ i0 + 1 < (j0 + 1) * (j0 + 1)
Proof step 14:
0 ≤ i0, 0 < i0 → 0 < j ∧ j * j ≤ i0 ∧ i0 < (j + 1) * (j + 1) ⊦ 0 < i0, ∃ j0. 0 < j0 ∧ j0 * j0 ≤ i0 + 1 ∧ i0 + 1 < (j0 + 1) * (j0 + 1)

Rule argument

fma: 0 < i0

Additional information

Used formulas: 0 < i0