Commit 2025-12-16 13:45 047c422f

View on Github →

feat(Geometry/Convex/Cone): define and characterize generating convex cone (#32300) Define the notion of a generating convex cone. Prove some initial simple lemmas about generating cones.

Estimated changes

Modified Mathlib/Geometry/Convex/Cone/Basic.lean

added theorem ConvexCone.IsGenerating.isReproducing

added theorem ConvexCone.IsGenerating.mono

added theorem ConvexCone.IsGenerating.of_top_le_span

added theorem ConvexCone.IsGenerating.span_eq_top

added theorem ConvexCone.IsGenerating.top_le_span

added def ConvexCone.IsGenerating

added theorem ConvexCone.IsReproducing.isGenerating

added theorem ConvexCone.IsReproducing.of_univ_subset

added theorem ConvexCone.IsReproducing.sub_eq_univ

added def ConvexCone.IsReproducing

added theorem ConvexCone.isGenerating_bot

added theorem ConvexCone.isGenerating_bot_iff

added theorem ConvexCone.isGenerating_iff_isReproducing

added theorem ConvexCone.isGenerating_top