Theorems · Theorem · convex and discrete geometry
ConvexBody.zero_mem_of_symmetric
∀ {V : Type u_1} [inst : TopologicalSpace V] [inst_1 : AddCommGroup V] [inst_2 : Module ℝ V] (K : ConvexBody V),
(∀ x ∈ K, -x ∈ K) → 0 ∈ KA convex body that is symmetric contains 0.
- Defined in
- Mathlib.Analysis.Convex.Body
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- one_divproof · cited by 624
- lt_of_not_geproof · cited by 374
- neg_neg_of_posproof · cited by 227
- add_neg_cancelproof · cited by 213
- smul_negproof · cited by 181
Cited by1
Results whose statement or proof uses this declaration.