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Proof step 2 from proof square-le-one-01 (previous step)

sqrt(2 * i) ≤ 1, 0 < i ⊦ i = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: square-le-one seq: ⊦ 0 < i → (sqrt(i) ≤ 1 ↔ i < 4) subst: [i] → [2 * i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%nummult-ls: ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i); from specification int-div%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: 2 * i