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A path ψ is said to be an elementary deformation of ϕ (both with domain [a,b] ) if we can find a=x₀ < x₁ < … < x_n=b and convex open subsets C₁, …,C_n of D such that, whenever t ∈ [x_i−1,x_i] , we have both ϕ(t) ∈ C_i and ψ(t) ∈ C_i . For a holomorphic function f , we then have

⌠ ⌡ ψ  f(z) dz = ⌠ ⌡ ϕ  f(z) dz.

Compare homotopic.