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Proof step 22 from proof square-inject (previous step)

(i0 + j0) * (i0 + j0 + 1) + j0 * 2 = (i + j) * (i + j + 1) + j * 2, j ≤ i1 + j0, 0 ≤ i1 + j0, 0 ≤ i, 0 ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ i1 ⊦ i = i0 ∧ j = j0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: square-inject seq: i * (i + 1) + 2 * i0 = j * (j + 1) + 2 * j0, i0 ≤ i, j0 ≤ j, 0 ≤ i0, 0 ≤ j, 0 ≤ j0 ⊦ i = j ∧ i0 = j0 subst: [i, i0, j, j0] → [j + i, j, j0 + i0, j0] flags:

Additional information

Used simplifier rules: add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%numeq: ⊦ (* i2) * i + j = (* i1) * i + j0 ↔ (i2 - i1) * i + j = j0; from specification int-mult%zero-left: ⊦ 0 * i = 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-zero-rev: ⊦ 0 + i = i; from specification int-basic2%lep: ⊦ i ≤ i + j ↔ 0 ≤ j; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-gs: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0; from specification int-abs Used terms: j + i, j, j0 + i0, j0