Theorems · Theorem · order theory

ciInf_inf_eq

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

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by: 0 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ConditionallyCompleteLattice

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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_sup_eqproof · cited by 3

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