Theorems · Theorem · number theory
iSup_unpair
∀ {α : Type u_1} [inst : CompleteLattice α] (f : ℕ → ℕ → α), ⨆ n, f (Nat.unpair n).1 (Nat.unpair n).2 = ⨆ i, ⨆ j, f i j- Defined in
- Mathlib.Data.Nat.Pairing
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Nat.unpairstatement and proof · cited by 67
- iSup_prodproof · cited by 10
- Function.Surjective.iSup_compproof · cited by 9
- Nat.surjective_unpairproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- mem_countableSupClosure_iff_iSupproof · cited by 1
- Set.iUnion_unpairproof · cited by 1
- InfClosed.countableSupClosureproof · cited by 0