Theorems · Theorem · order theory
Disjoint.mono_left
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderBot α] {a b c : α}, a ≤ b → Disjoint b c → Disjoint a c- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderBot
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.
- PartialOrderstatement and proof · cited by 6,410
- Disjointstatement · cited by 2,201
- le_rflproof · cited by 1,558
- OrderBotstatement and proof · cited by 1,055
- Disjoint.monoproof · cited by 69
Cited by50
Results whose statement or proof uses this declaration.
- Set.disjoint_of_subset_leftproof · cited by 17
- sdiff_eq_leftproof · cited by 15
- Disjoint.closure_leftproof · cited by 6
- IsCompact.disjoint_nhdsSet_leftproof · cited by 6
- Disjoint.inf_leftproof · cited by 5
- LE.le.disjoint_compl_rightproof · cited by 5
- le_sdiffproof · cited by 4
- disjoint_memPartitionproof · cited by 3
- Disjoint.inf_left'proof · cited by 3
- Matroid.contract_delete_commproof · cited by 3
- Metric.ball_disjoint_ballproof · cited by 3
- iSupIndep.le_iff_eq_of_iSup_eq_topproof · cited by 3