Theorems · Theorem · order theory
sup_iSup_nat_succ
∀ {α : Type u_1} [inst : CompleteLattice α] (u : ℕ → α), u 0 ⊔ ⨆ i, u (i + 1) = ⨆ i, u i- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_rangeproof · cited by 24
- iSup_unionproof · cited by 8
- iSup_univproof · cited by 8
- iSup_singletonproof · cited by 7
- Nat.zero_union_range_succproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Nat.iSup_lt_succ'proof · cited by 3
- Language.one_add_self_mul_kstar_eq_kstarproof · cited by 2
- Set.union_iUnion_nat_succproof · cited by 0