Theorems · Theorem · order theory
SetRel.prodMk_mem_comp
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {R : SetRel α β} {S : SetRel β γ} {a : α} {b : β} {c : γ},
(a, b) ∈ R → (b, c) ∈ S → (a, c) ∈ R.comp S- Defined in
- Mathlib.Data.Rel
- Cited by
- 12 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.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetRelstatement and proof · cited by 581
- SetRel.compstatement · cited by 136
Cited by12
Results whose statement or proof uses this declaration.
- UniformSpace.mem_ball_compproof · cited by 5
- CauchyFilter.denseRange_pureCauchyproof · cited by 5
- Equicontinuous.comap_uniformFun_eqproof · cited by 3
- tendsto_comp_of_locally_uniform_limit_withinproof · cited by 3
- uniformContinuousOn_of_uniform_approx_of_uniformContinuousOnproof · cited by 2
- continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAtproof · cited by 2
- IsCompact.mem_uniformity_of_prodproof · cited by 2
- le_nhds_of_cauchy_adhp_auxproof · cited by 2
- TendstoUniformlyOnFilter.uniformCauchySeqOnFilterproof · cited by 2
- equicontinuousWithinAt_iff_pairproof · cited by 1
- Uniform.exists_is_open_mem_uniformity_of_forall_mem_eqproof · cited by 1
- completeSpace_extensionproof · cited by 0