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Theorems · Theorem · order theory

neg_sup

∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] [AddRightMono α] (a b : α), -(a ⊔ b) = -a ⊓ -b
Defined in
Mathlib.Algebra.Order.Group.Lattice
Cited by
3 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
LatticeAddGroupAddLeftMonoAddRightMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.neg_uIcc · cited by 2Set.neg_uIccnegPart_eq_neg_inf_zero · cited by 1negPart_eq_neg_inf_zeronegPart_max · cited by 0negPart_maxAddGroup · cited by 4410AddGroupLattice · cited by 916LatticeAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMonoOrderIso.map_sup · cited by 37OrderIso.map_supOrderIso.neg · cited by 27OrderIso.negneg_supCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.