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Proof step 5 from proof mod-nle (previous step)

j * i + i0 - j ≤ 0, i0 < i, j * i + i0 ≤ j, 0 ≤ i0, 0 < j, 0 < i ⊦ j * i + i0 - j = j * (i - 1) + i0, i = 1 ∧ i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: dist-sub-split seq: ⊦ (i - j) * j0 = i * j0 - j * j0 subst: [j0, j, i] → [j, 1, i] flags: rewrite, current

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2 Used terms: j, 1, i