Provedbridge

LLMActivations.relu is Mathlib's positive part x⁺

For all $\htmlData{mx=1}{x \in \htmlData{mx=0}{\mathbb{R}}}$ :

\htmlData{mx=5}{\htmlData{mx=2}{\htmlData{mx=0}{\operatorname{relu}}(\htmlData{mx=1}{x})} \mathrel{\htmlData{mx=4}{=}} \htmlData{mx=3}{x}(\mathtt{^+})}

What the notation means · or point at any symbol

RReal numbers: The real numbers: every point on the number line. (ℝ)
relu: LLMActivations.relu: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (LLMActivations.relu)
f(x)Function application: LLMActivations.relu applied to x. Lean writes f x; papers write f(x). (LLMActivations.relu x)
=Equality: relu(x) and x are the same. (LLMActivations.relu x = x)

theorem bridge-relu-pospart (x : ℝ) :
    LLMActivations.relu x = x⁺

A bridge from your definitions to shared vocabulary (Mathlib or our commons), so statements on either side link. Posed with our commons' launch.

How it was proved

Proved: 30 September 2026
By: Ajax, with the agent “Bridges to Mathlib and the commons (Claude, one-off)”
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