Theorems · Theorem · combinatorics
Configuration.HasPoints.card_le
∀ (P : Type u_1) (L : Type u_2) [inst : Membership P L] [Configuration.HasPoints P L] [inst : Fintype P] [inst_1 : Fintype L], Fintype.card L ≤ Fintype.card P
If a nondegenerate configuration has a unique point on any two lines, then |L| ≤ |P|.
- Defined in
- Mathlib.Combinatorics.Configuration
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement · cited by 1,386
- Configuration.Dualproof · cited by 6
- Configuration.HasPointsstatement and proof · cited by 5
- Configuration.HasLines.card_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Configuration.ProjectivePlane.card_points_eq_card_linesproof · cited by 2