Theorems · Theorem · order theory
inf_eq_left
∀ {α : Type u} [inst : SemilatticeInf α] {a b : α}, a ⊓ b = a ↔ a ≤ b- Defined in
- Mathlib.Order.Lattice
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- SemilatticeInf
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.
- SemilatticeInfstatement and proof · cited by 634
- inf_le_leftproof · cited by 286
- le_inf_iffproof · cited by 48
- Std.ge_reflproof · cited by 23
- ge_antisymm_iffproof · cited by 8
Cited by41
Results whose statement or proof uses this declaration.
- inf_of_le_leftproof · cited by 186
- Set.uIcc_of_leproof · cited by 54
- Set.inter_eq_leftproof · cited by 44
- Filter.map_comap_of_memproof · cited by 9
- nhdsWithin_eq_nhdsproof · cited by 8
- Finset.inter_eq_leftproof · cited by 7
- Set.uIoo_of_leproof · cited by 5
- Subgroup.map_subgroupOf_eq_of_leproof · cited by 4
- inf_indproof · cited by 4
- left_eq_infproof · cited by 4
- ProbabilityTheory.Kernel.isProper_iff_restrict_eq_indicator_smulproof · cited by 3
- min_eq_left_iffproof · cited by 3