Theorems · Theorem · order theory
ENat.iInf_eq_natCast_iff
∀ {ι : Sort u_1} {f : ι → ℕ∞} {n : ℕ}, ⨅ i, f i = ↑n ↔ (∃ i, f i = ↑n) ∧ ∀ (i : ι), ↑n ≤ f i- Defined in
- Mathlib.Data.ENat.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- ENatstatement and proof · cited by 4,985
- iInfstatement · cited by 1,690
- IsEmptyproof · cited by 759
- sInf_emptyproof · cited by 12
- iInf_of_isEmptyproof · cited by 10
- ciInf_eq_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ENat.iInf_eq_coe_iffproof · cited by 0