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Proof step 5 from proof square-le-06 (previous step)

i < 0, i * i ≤ i + 1 ⊦ i = 0, i = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i < 0 ∧ 0 < j → ¬ j ≤ i

Rule argument

spec: int-abs inst: name: zero-gels-02 seq: ⊦ i < 0 ∧ 0 < j → ¬ j ≤ i subst: [i, j] → [i + 1, i * i] flags: rewrite

Additional information

Used simplifier rules: zero-gr-01: ⊦ i < 0 → (0 < i * j ↔ j < 0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%mone-08: ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs Used terms: i + 1, i * i