Add new theorems and proofs

EasyLean/Basic.lean

@@ -1,12 +1,4 @@
-import Mathlib.Data.Real.Basic
-import Mathlib.Tactic.Linarith
+import EasyLean.Theorems.mathd_algebra_513
+import EasyLean.Theorems.eq_four
 
-theorem mathd_algebra_513
-  (a b : ℝ)
-  (h₀ : 3 * a + 2 * b = 5)
-  (h₁ : a + b = 2) :
-  a = 1 ∧ b = 1 := by
-  sorry
-
-theorem eq_four : ∀ a b c d : Nat, a = b → a = d → a = c → c = b := by
-  sorry
+-- Basic entry point that re-exports the core theorems for this project.

EasyLean/Theorems/eq_four.lean

@@ -0,0 +1,6 @@
+import Mathlib
+
+-- Equality transitivity helper that ignores an unused hypothesis.
+theorem eq_four : ∀ a b c d : Nat, a = b → a = d → a = c → c = b := by
+  intro a b c d hab had hac
+  exact hac.symm.trans hab

EasyLean/Theorems/mathd_algebra_513.lean

@@ -0,0 +1,6 @@
+import Mathlib
+
+-- Solves a 2x2 linear system with integer coefficients.
+theorem mathd_algebra_513
+    (a b : Real) (h0 : 3 * a + 2 * b = 5) (h1 : a + b = 2) : a = 1 ∧ b = 1 := by
+  constructor <;> linarith [h0, h1]

Main.lean

@@ -0,0 +1,3 @@
+import EasyLean.Basic
+
+-- Main executable entry point for the Lean project; ensures theorem modules compile.