Theorems · Theorem · order theory
ENat.toNat_sum
∀ {α : Type u_1} {s : Finset α} {f : α → ℕ∞}, (∀ a ∈ s, f a ≠ ⊤) → (∑ a ∈ s, f a).toNat = ∑ a ∈ s, (f a).toNatSeeing ℕ∞ as ℕ does not change their sum, unless one of the ℕ∞ is
infinity
- Defined in
- Mathlib.Data.ENat.BigOperators
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- Finset.sumstatement and proof · cited by 5,195
- ENatstatement and proof · cited by 4,985
- Finset.sum_congrproof · cited by 2,323
- ENat.toNatstatement and proof · cited by 143
- Nat.cast_sumproof · cited by 38
- ENat.natCast_toNatproof · cited by 11
- ENat.natCast_injproof · cited by 9
- ENat.sum_ne_topproof · cited by 1
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