Theorems · Theorem · order theory

add_ciInf

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

Defined in: Mathlib.Algebra.Order.Group.CompleteLattice
Cited by: 0 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Quot.sound
Assumes: AddGroup ConditionallyCompleteLattice Nonempty AddLeftMono

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Set.rangestatement and proof · cited by 4,705
AddGroupstatement and proof · cited by 4,410
iInfstatement · cited by 1,690
AddLeftMonostatement and proof · cited by 687
BddBelowstatement and proof · cited by 401
ConditionallyCompleteLatticestatement and proof · cited by 364
OrderIso.addLeftproof · cited by 18
OrderIso.map_ciInfproof · cited by 4

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