Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.of_comap_surjective
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] {C F : PointedCone R M} [inst_5 : AddCommGroup N]
[inst_6 : Module R N] {f : N →ₗ[R] M},
Function.Surjective ⇑f → (PointedCone.comap f F).IsFaceOf (PointedCone.comap f C) → F.IsFaceOf C- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 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.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- PartialOrderstatement and proof · cited by 6,410
- map_addproof · cited by 964
- IsOrderedRingstatement and proof · cited by 777
- map_smulproof · cited by 566
- PointedConestatement and proof · cited by 151
- PointedCone.IsFaceOfstatement and proof · cited by 34
Cited by1
Results whose statement or proof uses this declaration.
- PointedCone.isFaceOf_comap_iffproof · cited by 0