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Theorems · Theorem · order theory

neg_inf

∀ {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
4 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.

inf_add_sup · cited by 3inf_add_supSet.neg_uIcc · cited by 2Set.neg_uIccnegPart_min · cited by 1negPart_mindual_solid · cited by 0dual_solidAddGroup · cited by 4410AddGroupLattice · cited by 916LatticeAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMonoOrderIso.neg · cited by 27OrderIso.negOrderIso.map_inf · cited by 17OrderIso.map_infneg_infCITED BYCITES

Cites6

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

Cited by4

Results whose statement or proof uses this declaration.