Theorems · Theorem · order theory
Monotone.iSup_nat_add
∀ {α : Type u_1} [inst : CompleteLattice α] {f : ℕ → α}, Monotone f → ∀ (k : ℕ), ⨆ n, f (n + k) = ⨆ n, f n- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- Monotonestatement and proof · cited by 1,397
- CompleteLatticestatement and proof · cited by 1,048
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- iSup_monoproof · cited by 37
Cited by3
Results whose statement or proof uses this declaration.
- iSup_iInf_ge_nat_addproof · cited by 2
- Antitone.iInf_nat_addproof · cited by 1
- Monotone.iUnion_nat_addproof · cited by 0