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Proof step 9 from proof exdivmod (previous step)

0 ≤ i ∧ 0 < j → i = i0 * j + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < j ⊦ j = 0, ¬ i < 0 ∧ ¬ j < 0, ∃ i0, j0. i = i0 * j + j0 ∧ abs(j0) < abs(j)

User applied rule cut formula

And obtained the following new goals

Proof step 10:
j < 0, 0 ≤ i ∧ 0 < j → i = i0 * j + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < j ⊦ j = 0, ¬ i < 0 ∧ ¬ j < 0, ∃ i0, j0. i = i0 * j + j0 ∧ abs(j0) < abs(j)
Proof step 23:
0 ≤ i ∧ 0 < j → i = i0 * j + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < j ⊦ j < 0, j = 0, ¬ i < 0 ∧ ¬ j < 0, ∃ i0, j0. i = i0 * j + j0 ∧ abs(j0) < abs(j)

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0