Linear distributions are fundamental in the proof theory of linear logic:
(A ⊗ (B ⅋ C)) ⊸ ((A ⊗ B) ⅋ C).
The Modal Modus Ponens is given by:
□(φ → ψ), □φ ⊢ □ψ.
The gradient theorem reads as follows:
Let φ : U ⊆ ℝⁿ → ℝ and s is any curve from p to q. Then
φ(q) - φ(p) = ∫ₛ ∇φ(r) ∙ dr.