Theorems · Theorem · order theory
SetLike.coe_subset_coe
∀ {A : Type u_1} {B : Type u_2} [inst : SetLike A B] [inst_1 : LE A] [IsConcreteLE A B] {S T : A}, ↑S ⊆ ↑T ↔ S ≤ T- Defined in
- Mathlib.Data.SetLike.Basic
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- SetLikeLEIsConcreteLE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- SetLikestatement and proof · cited by 1,084
- IsConcreteLEstatement and proof · cited by 28
- IsConcreteLE.coe_subset_coe'proof · cited by 1
Cited by53
Results whose statement or proof uses this declaration.
- SetLike.coe_monoproof · cited by 18
- SetLike.coe_ssubset_coeproof · cited by 5
- Submodule.neg_leproof · cited by 3
- Algebra.adjoin_adjoin_of_towerproof · cited by 3
- Module.exists_basis_of_span_of_maximalIdeal_rTensor_injectiveproof · cited by 2
- PrimeSpectrum.comap_evalRingHom_basicOpenproof · cited by 2
- LieIdeal.map_comap_eqproof · cited by 2
- Subalgebra.iSupLift_inclusionproof · cited by 2
- IsAddFreimanHom.addRothNumber_monoproof · cited by 2
- IsSemiprimaryRing.inductionproof · cited by 2
- Nat.one_mem_span_iffproof · cited by 1
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1