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Proof step 1 from proof square-interval (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: square-ls-01: ⊦ 0 ≤ i ∧ 0 ≤ j → ((i * (i + 1)) / 2 < ((j + 1) * (j + 2)) / 2 ↔ i < j + 1);%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ler: ⊦ i ≤ i; from specification int-abs%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs