Theorems · Theorem · order theory

ciSup_add

∀ {ι : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : ConditionallyCompleteLattice G] [Nonempty ι] {f : ι → G}
  [AddRightMono G], BddAbove (Set.range f) → ∀ (a : G), (⨆ i, f i) + a = ⨆ i, f i + a

Defined in: Mathlib.Algebra.Order.Group.CompleteLattice
Cited by: 1 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Quot.sound
Assumes: AddGroup ConditionallyCompleteLattice Nonempty AddRightMono

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

Set.rangestatement and proof · cited by 4,705
AddGroupstatement and proof · cited by 4,410
iSupstatement · cited by 2,415
BddAbovestatement and proof · cited by 620
AddRightMonostatement and proof · cited by 367
ConditionallyCompleteLatticestatement and proof · cited by 364
OrderIso.addRightproof · cited by 16
OrderIso.map_ciSupproof · cited by 6

Cited by1

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ciSup_subproof · cited by 0