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Proof step 2 from proof modeqp-01 (previous step)

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

Rule argument

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

Additional information

Used simplifier rules: ⊦ ~ i = ~ j ↔ i = j; (s)% ⊦ i + j = i + i0 ↔ j = i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i, j, ~ j1, i0, ~ j0