Theorems · Theorem · order theory
Antitone.iInf_nat_add
∀ {α : Type u_1} [inst : CompleteLattice α] {f : ℕ → α}, Antitone f → ∀ (k : ℕ), ⨅ n, f (n + k) = ⨅ n, f n- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- Antitonestatement and proof · cited by 563
- Antitone.dual_rightproof · cited by 42
- Monotone.iSup_nat_addproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Antitone.iInter_nat_addproof · cited by 1