# HG changeset patch # User nipkow # Date 1574969887 -3600 # Node ID a25b6f79043f29a93f050e76f99dde01881ea995 # Parent df1d96114754df10f6169983e9852b6b412923c0# Parent 57bc95d2349106659892a04a617bfe6a445069e1 merged diff -r df1d96114754 -r a25b6f79043f src/HOL/Analysis/Abstract_Euclidean_Space.thy --- a/src/HOL/Analysis/Abstract_Euclidean_Space.thy Thu Nov 28 16:43:02 2019 +0000 +++ b/src/HOL/Analysis/Abstract_Euclidean_Space.thy Thu Nov 28 20:38:07 2019 +0100 @@ -4,7 +4,7 @@ section\Euclidean space and n-spheres, as subtopologies of n-dimensional space\ theory Abstract_Euclidean_Space -imports Homotopy Locally T1_Spaces +imports Homotopy Locally begin subsection \Euclidean spaces as abstract topologies\ diff -r df1d96114754 -r a25b6f79043f src/HOL/Analysis/Cartesian_Euclidean_Space.thy --- a/src/HOL/Analysis/Cartesian_Euclidean_Space.thy Thu Nov 28 16:43:02 2019 +0000 +++ b/src/HOL/Analysis/Cartesian_Euclidean_Space.thy Thu Nov 28 20:38:07 2019 +0100 @@ -5,7 +5,7 @@ section \Finite Cartesian Products of Euclidean Spaces\ theory Cartesian_Euclidean_Space -imports Cartesian_Space Derivative +imports Convex_Euclidean_Space Derivative begin lemma subspace_special_hyperplane: "subspace {x. x $ k = 0}" diff -r df1d96114754 -r a25b6f79043f src/HOL/Analysis/Derivative.thy --- a/src/HOL/Analysis/Derivative.thy Thu Nov 28 16:43:02 2019 +0000 +++ b/src/HOL/Analysis/Derivative.thy Thu Nov 28 20:38:07 2019 +0100 @@ -7,10 +7,6 @@ theory Derivative imports - Convex_Euclidean_Space - Abstract_Limits - Operator_Norm - Uniform_Limit Bounded_Linear_Function Line_Segment begin