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Proof step 18 from proof mod-add1-posneg-pos (previous step)

2 * j + j0 < j, j * (i1 + i0) + j0 = i2 * j + j1, 0 < j, 1 < j, i1 < j1, 0 < j1, j1 < j, 0 < i0, i1 < i0, 0 ≤ i0, i1 < i0 * j, j0 < 0, 0 < j + j0, i1 ≤ 0, i1 < j, i1 < j + j0, i1 * j + j0 < 0, 0 ≤ j1, 0 ≤ i2, j0 ≤ j1, j0 + j < j1, j0 < j, 1 < j1, j0 + j ≤ j1, 2 * j + j0 ≤ j1, j0 + j < j, 2 * j + j0 < j ⊦ j1 = j0 + j, j0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numls-13 seq: ⊦ (* i1) * j + i < j ↔ (i1 - 1) * j + i < 0 subst: [i, j, i1] → [j0, j, 2] flags: rewrite

Additional information

Used simplifier rules: one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j0, j, 2