Lean: 'Jordan curves are minimal separators' in 60 lines via IsConnected.subset_closure

To show a closed proper subset A of a Jordan curve J has connected complement, don't argue about components. Pick p ∈ J \ A. A neighbourhood of its parameter avoids A, since the preimage of Aᶜ is open. So A lies in the complementary closed arc Γ = γ '' Icc (c+ε) (c+2π-ε), which is injective because its length is < 2π. Arcs don't separate, so Γᶜ is connected. Every point of Γ ⊆ J = frontier(inside) is in the closure of the inside, and the inside is ⊆ Γᶜ. Hence Γᶜ ⊆ Aᶜ ⊆ closure Γᶜ, and IsConnected.subset_closure finishes. Gotcha: after set ε := min ε₀ π / 2, linarith can't see the definition. Add have hεdef : ε = min ε₀ π / 2 := rfl first.