Theorems · Theorem · logic and foundations
Set.mem_of_mem_inter_left
∀ {α : Type u} {x : α} {a b : Set α}, x ∈ a ∩ b → x ∈ a- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by10
Results whose statement or proof uses this declaration.
- AffineSubspace.ext_of_direction_eqproof · cited by 11
- IsPreirreducible.imageproof · cited by 3
- not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioiproof · cited by 2
- measurable_iSup_of_lowerSemicontinuousproof · cited by 1
- exists_gt_t2spaceproof · cited by 1
- IsConnected.unionproof · cited by 1
- LocallyFinite.exists_finset_nhds_support_subsetproof · cited by 1
- FirstOrder.Language.ClosedUnder.interproof · cited by 1
- Vitali.exists_disjoint_covering_aeproof · cited by 1
- LocallyFinite.exists_finset_nhds_mulSupport_subsetproof · cited by 0