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Proof step 7 from proof square-eq-01 (previous step)

i * i + i = j * j + j, 0 ≤ i, 0 ≤ j, j < i, 0 < i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: square-ls-02 seq: ⊦ 0 ≤ i ∧ 0 ≤ j → (i * (i + 1) < j * (j + 1) ↔ i < j) subst: [j, i] → [i, j] flags: rewrite, current

Additional information

Used simplifier rules: dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%irref: ⊦ ¬ i < i; from specification int-basic1 Used terms: i, j