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Proof step 17 from proof square-le-one (previous step)

1 < (sqrt(i) + 1)^2, 0 < (sqrt(i) + 1)^2, sqrt(i) ^2 < (sqrt(i) + 1)^2, 2 ^2 < (sqrt(i) + 1)^2, i < (sqrt(i) + 1)^2, sqrt(i) ^2 ≤ i, 0 ≤ i, 2 ^2 ≤ i, sqrt(i) ≤ 1, 0 < i, sqrt(i) < (sqrt(i) + 1)^2 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: two-ls-pospos seq: ⊦ 0 ≤ i ∧ 0 ≤ j → (i ^2 < j ^2 ↔ i < j) subst: [j, i] → [sqrt(i) + 1, 2] flags: rewrite, current

Additional information

Used simplifier rules: square-not-neg: ⊦ 0 ≤ i → ¬ sqrt(i) < 0;%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; 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%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs Used terms: sqrt(i) + 1, 2