Theorems · Theorem · order theory
subset_trans
∀ {α : Type u_1} [UsesSetNotationForOrder α] [inst : Preorder α] {a b c : α}, a ⊆ b → b ⊆ c → a ⊆ cSet notation form of le_trans
- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
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.
Cited by63
Results whose statement or proof uses this declaration.
- Matroid.closure_subset_closureproof · cited by 24
- MvPolynomial.mem_range_map_iff_coeffs_subsetproof · cited by 5
- PairReduction.finset_logSizeBallSeq_subset_logSizeBallSeq_initproof · cited by 4
- ChainCompletePartialOrder.bot_isAdmissibleproof · cited by 4
- Set.Countable.isLindelof_biUnionproof · cited by 4
- TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompactproof · cited by 3
- Convex.helly_theorem'proof · cited by 3
- Topology.RelCWComplex.cellFrontier_subset_skeletonLTproof · cited by 3
- rieszContentAux_unionproof · cited by 2
- MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
- Complex.subfield_eq_of_closedproof · cited by 2
- ChainCompletePartialOrder.IsExtremePt.bot_eq_of_le_or_map_leproof · cited by 2