Theorems · Theorem · order theory
sup_inf_left
∀ {α : Type u} [inst : DistribLattice α] (a b c : α), a ⊔ b ⊓ c = (a ⊔ b) ⊓ (a ⊔ c)- Defined in
- Mathlib.Order.Lattice
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- DistribLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_antisymmproof · cited by 2,068
- DistribLatticestatement and proof · cited by 150
- sup_inf_leproof · cited by 1
- le_sup_infproof · cited by 1
Cited by22
Results whose statement or proof uses this declaration.
- inf_sup_leftproof · cited by 28
- sup_inf_rightproof · cited by 22
- sdiff_supproof · cited by 7
- le_of_inf_le_sup_leproof · cited by 4
- sdiff_sdiff_rightproof · cited by 4
- Finset.inf_sup_distrib_leftproof · cited by 3
- symmDiff_sup_infproof · cited by 2
- IsCompl.sup_infproof · cited by 2
- inf_sdiffproof · cited by 2
- sup_eq_sdiff_sup_sdiff_sup_infproof · cited by 2
- Coheyting.boundary_le_boundary_sup_sup_boundary_inf_leftproof · cited by 2
- max_min_distrib_leftproof · cited by 2