Theorems · Theorem · geometry

Projectivization.Subspace.subset_span_trans

∀ {K : Type u_1} {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  {S T U : Set (Projectivization K V)},
  S ⊆ ↑(Projectivization.Subspace.span T) →
    T ⊆ ↑(Projectivization.Subspace.span U) → S ⊆ ↑(Projectivization.Subspace.span U)

Defined in: Mathlib.LinearAlgebra.Projectivization.Subspace
Cited by: 0 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module

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Setstatement and proof · cited by 53,352
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
SetLike.coestatement and proof · cited by 8,199
DivisionRingstatement and proof · cited by 1,062
GaloisInsertion.gcproof · cited by 137
Projectivizationstatement and proof · cited by 111
Projectivization.Subspacestatement · cited by 34
Projectivization.Subspace.spanstatement and proof · cited by 16
Projectivization.Subspace.giproof · cited by 7
GaloisConnection.le_u_l_transproof · cited by 2

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