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Proof step 21 from proof div-shift-two (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j, 2 * i1, 1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i + j < i + i0 ↔ j < i0; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, 2 * i1, 1