Theorems · Theorem · logic and foundations
Set.union_eq_right
∀ {α : Type u} {s t : Set α}, s ∪ t = t ↔ s ⊆ t- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- sup_eq_rightproof · cited by 53
Cited by14
Results whose statement or proof uses this declaration.
- Set.union_eq_self_of_subset_leftproof · cited by 13
- MeasureTheory.addContent_sdiff_of_ne_topproof · cited by 3
- frontier_subset_iff_isClosedproof · cited by 2
- IntermediateField.sSup_toSubfieldproof · cited by 1
- Submodule.iUnion_ssubset_of_forall_ne_top_of_card_ltproof · cited by 1
- AddSemigroupIdeal.coe_closure'proof · cited by 1
- Algebra.sSup_toSubsemiringproof · cited by 1
- SemigroupIdeal.coe_closure'proof · cited by 1
- IntermediateField.sup_toSubfieldproof · cited by 1
- Algebra.sup_toSubsemiringproof · cited by 0
- Circle.not_isPreconnected_compl_pairproof · cited by 0
- Topology.IsInducing.le_functorObj_iffproof · cited by 0