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Proof step 6 from proof square-ls-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i < j ∧ j ≤ j0 → i < j0

Rule argument

spec: int-abs inst: name: forward-lsle seq: ⊦ i < j ∧ j ≤ j0 → i < j0 subst: [i, j, j0] → [i + i * i, j + j * j, j + i * i] flags: rewrite

Additional information

Used simplifier rules: square-le: ⊦ i * i ≤ j * j ↔ abs(i) ≤ abs(j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%lep-02: ⊦ i + j ≤ i + j0 ↔ j ≤ j0; from specification int-abs%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i + i * i, j + j * j, j + i * i