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Proof step 3 from proof square-not-neg-03 (previous step)

sqrt(2 * i) < i, 0 < i, sqrt(2 * i) ≤ 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 ≤ i → (sqrt(i) ≤ 0 ↔ i = 0)

Rule argument

spec: <toplevel> name: square-not-neg-02 seq: ⊦ 0 ≤ i → (sqrt(i) ≤ 0 ↔ i = 0) subst: [i] → [2 * i] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 2 * i = 0 ↔ i = 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used terms: 2 * i