Theorems · Theorem · order theory
inf_inf_inf_comm
∀ {α : Type u} [inst : SemilatticeInf α] (a b c d : α), a ⊓ b ⊓ (c ⊓ d) = a ⊓ c ⊓ (b ⊓ d)- Defined in
- Mathlib.Order.Lattice
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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_assocproof · cited by 53
- inf_left_commproof · cited by 9
Cited by13
Results whose statement or proof uses this declaration.
- inf_inf_distrib_leftproof · cited by 3
- inf_inf_distrib_rightproof · cited by 3
- Set.inter_inter_inter_commproof · cited by 2
- bihimp_triangleproof · cited by 1
- Finset.infs_infs_infs_commproof · cited by 0
- min_min_min_commproof · cited by 0
- Set.infs_infs_infs_commproof · cited by 0
- Subgroup.inf_subgroupOf_inf_normal_of_leftproof · cited by 0
- Subgroup.inf_subgroupOf_inf_normal_of_rightproof · cited by 0
- AddSubgroup.inf_addSubgroupOf_inf_normal_of_leftproof · cited by 0
- AddSubgroup.inf_addSubgroupOf_inf_normal_of_rightproof · cited by 0
- Finset.inf_infproof · cited by 0