Theorems · Theorem · logic and foundations
Set.union_eq_left
∀ {α : Type u} {s t : Set α}, s ∪ t = s ↔ t ⊆ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 6 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_leftproof · cited by 71
Cited by6
Results whose statement or proof uses this declaration.
- Set.union_eq_self_of_subset_rightproof · cited by 25
- Unitization.quasispectrum_eq_spectrum_inrproof · cited by 4
- BoxIntegral.Prepartition.iUnion_filter_notproof · cited by 2
- Filter.iInf_sets_inductproof · cited by 1
- AlgebraicGeometry.Scheme.zeroLocus_biInf_of_nonemptyproof · cited by 1
- Set.image_val_union_self_right_eqproof · cited by 0