Theorems · Theorem · order theory
Set.insert_subset_insert
∀ {α : Type u_1} {s t : Set α} {a : α}, s ⊆ t → insert a s ⊆ insert a t- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
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 by18
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.compproof · cited by 18
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5
- Matroid.fundCircuit_subset_insertproof · cited by 5
- HasFPowerSeriesWithinOnBall.monoproof · cited by 4
- HasFPowerSeriesWithinOnBall.changeOriginproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.IsBasis.iUnion_isBasis_iUnionproof · cited by 2
- Matroid.exists_isCircuit_of_mem_closureproof · cited by 2
- exists_of_linearIndepOn_of_finite_spanproof · cited by 1
- Function.range_eq_image_or_of_mulSupport_subsetproof · cited by 1
- Function.range_eq_image_or_of_support_subsetproof · cited by 1
- Matroid.IsBase.compl_inter_isBasis_of_inter_isBasisproof · cited by 1