midpoint_self
∀ (R : Type u_1) {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : Invertible 2] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] (x : P), midpoint R x x = x- Cited by
- 8 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Ringstatement and proof · cited by 7,463
- AddTorsorstatement and proof · cited by 1,657
- Invertiblestatement and proof · cited by 549
- Invertible.invOfproof · cited by 268
- midpointstatement · cited by 123
- AffineMap.lineMap_same_applyproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- midpoint_sub_addproof · cited by 2
- Urysohns.CU.approx_of_mem_Cproof · cited by 2
- Urysohns.CU.approx_of_notMem_Uproof · cited by 2
- EuclideanGeometry.oangle_midpoint_leftproof · cited by 1
- EuclideanGeometry.oangle_midpoint_rightproof · cited by 1
- midpoint_add_selfproof · cited by 0
- EuclideanGeometry.Sphere.center_mem_affineSpan_pair_iff_isDiameterproof · cited by 0