AffineMap.lineMap_rev_mem_affineSpan_pair
∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] (r : k) (p₁ p₂ : P), (AffineMap.lineMap p₂ p₁) r ∈ line[k, p₁, p₂]A combination of two points expressed with lineMap (with the two points reversed) lies in
their affine span.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement · cited by 871
- AffineMapstatement · cited by 674
- affineSpanstatement · cited by 417
- AffineMap.lineMapstatement · cited by 254
- left_mem_affineSpan_pairproof · cited by 15
- right_mem_affineSpan_pairproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- smul_vsub_rev_vadd_mem_affineSpan_pairproof · cited by 1