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Theorems · Definition · combinatorics

Configuration.HasPoints.hasLines

{P : Type u_1} →
  {L : Type u_2} →
    [inst : Membership P L] →
      [Configuration.HasPoints P L] →
        [inst_2 : Fintype P] → [inst_3 : Fintype L] → Fintype.card P = Fintype.card L → Configuration.HasLines P L

If a nondegenerate configuration has a unique point on any two lines, and if |P| = |L|, then there is a unique line through any two points.

Defined in
Mathlib.Combinatorics.Configuration
Cited by
0 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MembershipConfiguration.HasPointsFintypeFintype
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Fintype · cited by 7736FintypeFintype.card · cited by 1386Fintype.cardConfiguration.Dual · cited by 6Configuration.DualConfiguration.HasLines · cited by 6Configuration.HasLinesConfiguration.HasPoints · cited by 5Configuration.HasPointsConfiguration.HasPoints.mkPoint · cited by 3HasPoints.mkPointConfiguration.HasLines.hasPoints · cited by 0HasLines.hasPointsHasPoints.hasLinesCITED BYCITES

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