Theorems · Theorem · combinatorics
Configuration.HasLines.pointCount_le_lineCount
∀ {P : Type u_1} {L : Type u_2} [inst : Membership P L] [Configuration.HasLines P L] {p : P} {l : L},
p ∉ l → ∀ [Finite { l // p ∈ l }], Configuration.pointCount P l ≤ Configuration.lineCount L p- Defined in
- Mathlib.Combinatorics.Configuration
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Fintype.cardproof · cited by 1,386
- Nat.cardproof · cited by 844
- Infiniteproof · cited by 352
- nonempty_fintypeproof · cited by 261
- Nat.card_eq_fintype_cardproof · cited by 200
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- Fintype.card_le_of_injectiveproof · cited by 19
- Configuration.lineCountstatement and proof · cited by 11
- Configuration.pointCountstatement and proof · cited by 11
- Configuration.HasLinesstatement and proof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Configuration.HasLines.lineCount_eq_pointCountproof · cited by 3
- Configuration.HasLines.card_leproof · cited by 2
- Configuration.HasLines.exists_bijective_of_card_eqproof · cited by 1
- Configuration.HasPoints.lineCount_le_pointCountproof · cited by 0