Theorems · Definition · order theory
ClosureOperator.conjBy
{α : Type u_4} →
{β : Type u_5} → [inst : Preorder α] → [inst_1 : Preorder β] → ClosureOperator α → α ≃o β → ClosureOperator βIf c is a closure operator on α and e an order-isomorphism
between α and β then e ∘ c ∘ e⁻¹ is a closure operator on β.
- Defined in
- Mathlib.Order.Closure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- OrderIsostatement and proof · cited by 874
- OrderIso.symmproof · cited by 475
- ClosureOperatorstatement and proof · cited by 371
- OrderHomClass.toOrderHomproof · cited by 44
- ClosureOperator.IsClosedproof · cited by 38
- OrderIso.conjproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- OrderIso.equivClosureOperatorproof · cited by 2
- ClosureOperator.conjBy_applystatement and proof · cited by 0
- ClosureOperator.conjBy_reflstatement · cited by 0
- ClosureOperator.conjBy_transstatement · cited by 0
- OrderIso.equivClosureOperator_applystatement · cited by 0
- OrderIso.equivClosureOperator_symm_applystatement · cited by 0