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Proof step 15 from proof div-shift-two (previous step)

i0 * j + j0 < (1 + 2 * i0 / 2) * j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i0 ⊦ j = 0, i0 = 2 * i0 / 2

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-elim-pospos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [i0, 2, i, j1] flags: rewrite, current

Additional information

Used simplifier rules: numeq-01: ⊦ (* i2) * i = (* i1) * i + j0 ↔ (i2 - i1) * i = j0; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%ls-dist-01: ⊦ i * (j + i0) + j1 < i * (j0 + i0) ↔ i * j + j1 < i * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); from specification int-abs Used terms: i0, 2, i, j1