feat: Add low dim U(1)

HepLean/AnomalyCancellation/PureU1/LowDim/One.lean

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+/-
+Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license.
+Authors: Joseph Tooby-Smith
+-/
+import HepLean.AnomalyCancellation.PureU1.Permutations
+/-!
+# The Pure U(1) case with 1 fermion
+
+We show that in this case the charge must be zero.
+-/
+
+universe v u
+
+open Nat
+open  Finset
+
+namespace PureU1
+
+variable {n : ℕ}
+
+namespace One
+
+theorem solEqZero (S : (PureU1 1).LinSols) : S = 0 := by
+  apply ACCSystemLinear.LinSols.ext
+  have hLin := pureU1_linear S
+  simp at hLin
+  funext i
+  simp at i
+  rw [show i = (0 : Fin 1) by omega]
+  exact hLin
+
+end One
+
+end PureU1