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Coppelius.softmax is our commons' Commons.softmax

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

\htmlData{mx=3}{\htmlData{mx=0}{\operatorname{softmax}}(\htmlData{mx=1}{z}, \htmlData{mx=2}{i})} \mathrel{\htmlData{mx=8}{=}} \htmlData{mx=7}{\htmlData{mx=4}{\operatorname{softmax}}(\htmlData{mx=5}{z}, \htmlData{mx=6}{i})}

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)
softmax: Coppelius.softmax: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (Coppelius.softmax)
=Equality: softmax(z, i) and softmax(z, i) are the same. (Coppelius.softmax z i = Commons.softmax…)
RReal numbers: The real numbers: every point on the number line. (ℝ)

theorem bridge-coppelius-softmax-commons-softmax {n : ℕ} (z : Fin n → ℝ) (i : Fin n) :
    Coppelius.softmax z i = Commons.softmax z i

Found by our verifier when coppelius was published: Coppelius.softmax equals our commons' Commons.softmax, 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

Coppelius.softmax is our commons' Commons.softmax

How it was proved

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