Theorems · Definition · geometry
Submodule.toAffineSubspace
{k : Type u_1} →
{V : Type u_2} →
[inst : Ring k] → [inst_1 : AddCommGroup V] → [inst_2 : Module k V] → Submodule k V → AffineSubspace k VReinterprets p : Submodule k V as an AffineSubspace k V.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- AffineSubspacestatement · cited by 871
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.mem_toAffineSubspacestatement · cited by 1
- NumberField.mixedEmbedding.volume_eq_zeroproof · cited by 1
- affineSpan_le_toAffineSubspace_spanstatement · cited by 1
- NumberField.mixedEmbedding.realSpace.volume_eq_zeroproof · cited by 1
- AffineSubspace.direction_eq_self_iff_zero_memstatement and proof · cited by 0
- Submodule.toAffineSubspace_directionstatement and proof · cited by 0