Theorems · Theorem · order theory
Set.compl_subset_compl
∀ {α : Type u_1} {s t : Set α}, sᶜ ⊆ tᶜ ↔ t ⊆ s- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Compl.complstatement · cited by 2,925
- compl_le_compl_iff_leproof · cited by 5
Cited by50
Results whose statement or proof uses this declaration.
- Bornology.IsBounded.subsetproof · cited by 45
- Filter.hasBasis_cocompactproof · cited by 14
- PrimeSpectrum.isTopologicalBasis_basic_opensproof · cited by 11
- IsOpen.inter_closureproof · cited by 8
- Filter.hasBasis_coclosedCompactproof · cited by 8
- aeSeq.mk_eq_fun_of_mem_aeSeqSetproof · cited by 5
- hasBasis_coLindelofproof · cited by 5
- Filter.coclosedCompact_eq_cocompactproof · cited by 5
- IsOpenMap.preimage_closure_subset_closure_preimageproof · cited by 5
- MonotoneOn.countable_not_continuousWithinAtproof · cited by 3
- IsPreconnected.subset_of_closure_inter_subsetproof · cited by 3
- aeSeq.prop_of_mem_aeSeqSetproof · cited by 3