Theorems · Theorem · order theory

ciInf_mono

∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {f g : ι → α},
  BddBelow (Set.range f) → (∀ (x : ι), f x ≤ g x) → iInf f ≤ iInf g

The indexed infimum of two functions are comparable if the functions are pointwise comparable

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by: 2 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ConditionallyCompleteLattice

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Cites5

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
iInfstatement · cited by 1,690
BddBelowstatement and proof · cited by 401
ConditionallyCompleteLatticestatement and proof · cited by 364
ciSup_monoproof · cited by 9

Cited by2

Results whose statement or proof uses this declaration.

Finite.ciInf_monoproof · cited by 0
schnirelmannDensity_le_of_subsetproof · cited by 0