diff --git a/FormalBook/Chapter_02.lean b/FormalBook/Chapter_02.lean index 5531b26..810595b 100644 --- a/FormalBook/Chapter_02.lean +++ b/FormalBook/Chapter_02.lean @@ -15,7 +15,6 @@ limitations under the License. Authors: Moritz Firsching -/ -import Mathlib.Algebra.Lie.OfAssociative import Mathlib.Analysis.Convex.SpecificFunctions.Basic import Mathlib.Analysis.Convex.SpecificFunctions.Deriv import Mathlib.Data.Nat.Choose.Factorization @@ -38,7 +37,7 @@ formalized by Patrick Stevens and Bolton Bailey. -/ open scoped BigOperators -namespace chapter02 +namespace chapter2 open Real @@ -226,4 +225,4 @@ theorem exists_prime_lt_and_le_two_mul (n : ℕ) (hn0 : n ≠ 0) : -end chapter02 +end chapter2 diff --git a/blueprint/src/chapter/chapter02.tex b/blueprint/src/chapter/chapter02.tex index c90eda7..cede05b 100644 --- a/blueprint/src/chapter/chapter02.tex +++ b/blueprint/src/chapter/chapter02.tex @@ -1 +1,13 @@ \chapter{Bertrand's postulate} + +\begin{theorem} + \label{thm:bertrands_postulate} + \lean{chapter2.exists_prime_lt_and_le_two_mul} + \leanok + For any positive natural number, there is a prime which is greater than + it, but no more than twice as large. +\end{theorem} +\begin{proof} + \leanok + TODO: make this follow the book proof more closely! +\end{proof} \ No newline at end of file