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Theorems · Theorem · combinatorics

Configuration.ProjectivePlane.one_lt_order

∀ (P : Type u_1) (L : Type u_2) [inst : Membership P L] [inst_1 : Configuration.ProjectivePlane P L] [Finite P]
  [Finite L], 1 < Configuration.ProjectivePlane.order P L
Defined in
Mathlib.Combinatorics.Configuration
Cited by
2 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MembershipConfiguration.ProjectivePlaneFiniteFinite
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Configuration.ProjectivePlane.two_lt_lineCount · cited by 0ProjectivePlane.two_lt_li…Configuration.ProjectivePlane.two_lt_pointCount · cited by 0ProjectivePlane.two_lt_po…Fintype · cited by 7736FintypeFinite · cited by 3029Finitenonempty_fintype · cited by 261nonempty_fintypeNat.card_eq_fintype_card · cited by 200Nat.card_eq_fintype_cardadd_lt_add_iff_right · cited by 42add_lt_add_iff_rightConfiguration.ProjectivePlane · cited by 14Configuration.ProjectiveP…Configuration.ProjectivePlane.order · cited by 6ProjectivePlane.orderConfiguration.ProjectivePlane.exists_config · cited by 5ProjectivePlane.exists_co…Configuration.HasPoints.mkPoint · cited by 3HasPoints.mkPointConfiguration.ProjectivePlane.pointCount_eq · cited by 3ProjectivePlane.pointCoun…Fintype.two_lt_card_iff · cited by 3Fintype.two_lt_card_iffConfiguration.HasPoints.mkPoint_ax · cited by 2HasPoints.mkPoint_axProjectivePlane.one_lt_orderCITED BYCITES

Cites12

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Cited by2

Results whose statement or proof uses this declaration.