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Theorems · Theorem · order theory

sup_add

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

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

abs_nonneg · cited by 168abs_nonnegposPart_add_negPart · cited by 3posPart_add_negPartnegPart_add_posPart · cited by 0negPart_add_posPartAddGroup · cited by 4410AddGroupLattice · cited by 916LatticeAddRightMono · cited by 367AddRightMonoOrderIso.map_sup · cited by 37OrderIso.map_supOrderIso.addRight · cited by 16OrderIso.addRightsup_addCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.