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Proof step 11 from proof mod-add1-posneg-neg (previous step)

j * (i1 + i0) + j0 = i2 * j + j1, i2 * j + j1 < 0, i2 < j, i2 ≤ 0, j1 < j, j1 ≤ 0, i1 * j + j0 < 0, i1 < j, i1 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, abs(j0) < j, 0 ≤ i0, abs(j1) < j ⊦ 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] → [i2, j, j1, i0 + i1, j0] flags: []

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i2, j, j1, i0 + i1, j0