Theorems · Theorem · order theory
GaloisInsertion.gc
∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α}
(self : GaloisInsertion l u), GaloisConnection l uThe Galois connection associated to a Galois insertion.
- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 137 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 7 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- GaloisConnectionstatement · cited by 253
- GaloisInsertionstatement and proof · cited by 35
Cited by137
Results whose statement or proof uses this declaration.
- GaloisInsertion.l_u_eqproof · cited by 37
- Submodule.span_emptyproof · cited by 29
- Submodule.span_unionproof · cited by 23
- CategoryTheory.Sieve.le_generateproof · cited by 20
- PrimeSpectrum.zeroLocus_spanproof · cited by 17
- MonoidHom.map_closureproof · cited by 16
- MeasurableSpace.generateFrom_monoproof · cited by 15
- Polynomial.degree_le_natDegreeproof · cited by 14
- AddMonoidHom.map_mclosureproof · cited by 12
- GaloisInsertion.l_iSup_uproof · cited by 12
- Polynomial.natDegree_le_natDegreeproof · cited by 12
- GaloisInsertion.l_sup_uproof · cited by 11