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Proof step 2 from proof modeqp-03 (previous step)

i * j + j0 = i0 * j + j1, j < j1, j < j0, j < 0, j1 ≤ 0, j0 ≤ 0 ⊦ i = i0 ∧ j0 = j1

User applied rule apply lemma

And obtained the following new goals

Proof step 3:
i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i = i0 ∧ j0 = j1
Proof step 4:
i * j + j0 = i0 * j + j1, j < 0, j < j0, j < j1, j0 ≤ 0, j1 ≤ 0 ⊦ i = i0 ∧ j0 = j1, i * ~ j + j1 = i0 * ~ j + j0 ∧ abs(j1) < ~ j ∧ abs(j0) < ~ j

Rule argument

spec: <toplevel> name: modeqp-01 seq: i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i, ~ j, j1, i0, j0]

Additional information

Used terms: i, ~ j, j1, i0, j0