Theorems · Theorem · order theory
GaloisCoinsertion.u_inf_l
∀ {α : Type u} {β : Type v} {u : α → β} {l : β → α} [inst : SemilatticeInf α] [inst_1 : SemilatticeInf β]
(gi : GaloisCoinsertion l u) (a b : β), u (l a ⊓ l b) = a ⊓ b- Defined in
- Mathlib.Order.GaloisConnection.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInfSemilatticeInf
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.
- SemilatticeInfstatement and proof · cited by 634
- GaloisConnection.u_infproof · cited by 37
- GaloisCoinsertionstatement and proof · cited by 35
- GaloisCoinsertion.gcproof · cited by 22
- GaloisCoinsertion.u_l_eqproof · cited by 18
Cited by9
Results whose statement or proof uses this declaration.
- Subsemigroup.comap_inf_map_of_injectiveproof · cited by 0
- generateFrom_union_isOpenproof · cited by 0
- Subgroup.ofUnits_inf_unitsproof · cited by 0
- FirstOrder.Language.Substructure.comap_inf_map_of_injectiveproof · cited by 0
- AddSubsemigroup.comap_inf_map_of_injectiveproof · cited by 0
- Submodule.comap_inf_map_of_injectiveproof · cited by 0
- Submonoid.comap_inf_map_of_injectiveproof · cited by 0
- AddSubmonoid.comap_inf_map_of_injectiveproof · cited by 0
- AddSubgroup.ofAddUnits_inf_addUnitsproof · cited by 0