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Proof step 10 from proof mod-add-01 (previous step)

i * (i0 + 1) + j0 = i1 * i + j1, abs(j1) < i, i0 < i, i0 ≤ 0, j0 < i, j0 ≤ 0, i0 * i + j0 < 0, abs(j0) < i, 0 < i, j1 ≤ 0, j1 < i, i1 ≤ 0, i1 < i, i1 * i + j1 < 0 ⊦ j1 = j0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: 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] → [i1, i, j1, i0 + 1, j0] flags: []

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i1, i, j1, i0 + 1, j0