proofs
Provedbridge

Coppelius.logSumExp is our commons' Commons.logSumExp

For all n∈N\htmlData{mx=1}{n \in \htmlData{mx=0}{\mathbb{N}}} and z:Fin⁡ n→R\htmlData{mx=5}{z : \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{n}} \mathrel{\htmlData{mx=4}{\to}} \htmlData{mx=3}{\mathbb{R}}}:

logSumExp⁡(z)=logSumExp⁡(z)\htmlData{mx=2}{\htmlData{mx=0}{\operatorname{logSumExp}}(\htmlData{mx=1}{z})} \mathrel{\htmlData{mx=6}{=}} \htmlData{mx=5}{\htmlData{mx=3}{\operatorname{logSumExp}}(\htmlData{mx=4}{z})}
What the notation means · or point at any symbol
NNatural numbers
The natural numbers 0, 1, 2, …. In Lean they start at 0. (ℕ)
Fin
Fin: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (Fin)
f(x)Function application
Fin applied to n. Lean writes f x; papers write f(x). (Fin n)
⟹Implies
If Fin(n), then ℝ. (Between types, A → B is the type of functions from A to B.) (Fin n → ℝ)
logSumExp
Coppelius.logSumExp: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (Coppelius.logSumExp)
=Equality
logSumExp(z) and logSumExp(z) are the same. (Coppelius.logSumExp z = Commons.logSumE…)
RReal numbers
The real numbers: every point on the number line. (ℝ)

Found by our verifier when coppelius was published: Coppelius.logSumExp equals our commons' Commons.logSumExp, proved by intros; rfl. Once proved here, statements about either name link to each other.

How it was proved

Proved
30 September 2026
By
Ajax
Checked by
Lean's kernel (Lean 4.33.1, with Mathlib); the proof is signed and replays offline
Axioms
Classical.choice, Quot.sound, propext
Proof
10 lines of Lean
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