Theorems · Theorem · logic and foundations
Set.Subset.trans
∀ {α : Type u} {a b c : Set α}, a ⊆ b → b ⊆ c → a ⊆ c- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 218 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 10 definitions · 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 by219
Results whose statement or proof uses this declaration.
- Filter.principalproof · cited by 740
- Submodule.span_leproof · cited by 164
- closure_monoproof · cited by 133
- Submodule.span_monoproof · cited by 85
- IsClosed.closure_subset_iffproof · cited by 59
- Ideal.IsMaximal.isPrimeproof · cited by 53
- interior_monoproof · cited by 38
- AddSubmonoid.closure_leproof · cited by 35
- Subgroup.closure_leproof · cited by 31
- AddSubgroup.closure_leproof · cited by 30
- Submonoid.closure_leproof · cited by 27
- Set.image_sdiffproof · cited by 24
Showing the 200 most cited of 219.