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Theorems · Theorem · order theory

add_sup

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

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

abs_nonneg · cited by 168abs_nonnegposPart_sub_negPart · cited by 9posPart_sub_negPartposPart_add_negPart · cited by 3posPart_add_negPartinf_add_sup · cited by 3inf_add_supsup_eq_add_posPart_sub · cited by 0sup_eq_add_posPart_subnegPart_add_posPart · cited by 0negPart_add_posPartAddGroup · cited by 4410AddGroupLattice · cited by 916LatticeAddLeftMono · cited by 687AddLeftMonoOrderIso.map_sup · cited by 37OrderIso.map_supOrderIso.addLeft · cited by 18OrderIso.addLeftadd_supCITED BYCITES

Cites5

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Cited by6

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