Theorems · Theorem · order theory
GaloisConnection.le_u_l
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α},
GaloisConnection l u → ∀ (a : α), a ≤ u (l a)- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- le_rflproof · cited by 1,558
- GaloisConnectionstatement and proof · cited by 253
- GaloisConnection.le_uproof · cited by 15
Cited by52
Results whose statement or proof uses this declaration.
- Algebra.subset_adjoinproof · cited by 109
- GaloisConnection.monotone_lproof · cited by 76
- Submonoid.le_comap_mapproof · cited by 24
- CategoryTheory.Sieve.le_generateproof · cited by 20
- GaloisConnection.l_u_l_eq_lproof · cited by 19
- GaloisCoinsertion.u_l_eqproof · cited by 18
- GaloisConnection.u_l_u_eq_uproof · cited by 17
- Ideal.le_comap_mapproof · cited by 17
- Polynomial.degree_le_natDegreeproof · cited by 14
- Int.le_ceilproof · cited by 13
- Submodule.le_orthogonal_orthogonalproof · cited by 7
- GaloisConnection.l_uniqueproof · cited by 5