Theorems · Theorem · order theory
gc_lowerClosure_coe
∀ {α : Type u_1} [inst : Preorder α], GaloisConnection lowerClosure SetLike.coe- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- GaloisConnectionstatement · cited by 253
- LowerSetstatement and proof · cited by 230
- lowerClosurestatement · cited by 83
- lowerClosure_leproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- lowerClosure_iUnionproof · cited by 3
- lowerClosure_monoproof · cited by 1
- lowerClosure_unionproof · cited by 0
- giLowerClosureCoeproof · cited by 0