Theorems · Theorem · order theory
eq_of_inf_eq_sup_eq
∀ {α : Type u} [inst : DistribLattice α] {a b c : α}, b ⊓ a = c ⊓ a → b ⊔ a = c ⊔ a → b = c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- 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
- le_of_eqproof · cited by 366
- DistribLatticestatement and proof · cited by 150
- le_of_inf_le_sup_leproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- sdiff_uniqueproof · cited by 6
- Set.eq_of_mem_uIcc_of_mem_uIccproof · cited by 3
- sdiff_eq_sdiff_iff_inf_eq_infproof · cited by 2