diff --git a/archive/imo/imo1972_b2.lean b/archive/imo/imo1972_q5.lean similarity index 98% rename from archive/imo/imo1972_b2.lean rename to archive/imo/imo1972_q5.lean index 722405f8ccf67..7bd89bacc97d6 100644 --- a/archive/imo/imo1972_b2.lean +++ b/archive/imo/imo1972_q5.lean @@ -8,7 +8,7 @@ import data.real.basic import analysis.normed_space.basic /-! -# IMO 1972 B2 +# IMO 1972 Q5 Problem: `f` and `g` are real-valued functions defined on the real line. For all `x` and `y`, `f(x + y) + f(x - y) = 2f(x)g(y)`. `f` is not identically zero and `|f(x)| ≤ 1` for all `x`. @@ -30,7 +30,6 @@ example (f g : ℝ → ℝ) (y : ℝ) : ∥g(y)∥ ≤ 1 := begin - classical, set S := set.range (λ x, ∥f x∥), -- Introduce `k`, the supremum of `f`. let k : ℝ := Sup (S), @@ -86,7 +85,7 @@ begin end -/-- IMO 1972 B2 +/-- IMO 1972 Q5 Problem: `f` and `g` are real-valued functions defined on the real line. For all `x` and `y`, `f(x + y) + f(x - y) = 2f(x)g(y)`. `f` is not identically zero and `|f(x)| ≤ 1` for all `x`.