Theorems · Theorem · order theory
ofDual_preimage_latticeClosure
∀ {α : Type u_3} [inst : Lattice α] (s : Set α),
⇑OrderDual.ofDual ⁻¹' latticeClosure s = latticeClosure (⇑OrderDual.ofDual ⁻¹' s)- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Lattice
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.preimagestatement and proof · cited by 4,946
- Set.extproof · cited by 2,266
- OrderDualstatement and proof · cited by 927
- Latticestatement and proof · cited by 916
- OrderDual.toDualproof · cited by 481
- OrderDual.ofDualstatement and proof · cited by 400
- ClosureOperatorstatement · cited by 371
- Function.Surjective.forallproof · cited by 214
- Equiv.surjectiveproof · cited by 198
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