diff --git a/EasyLean/Basic.lean b/EasyLean/Basic.lean
index 305e1ca..40f4dd7 100644
--- a/EasyLean/Basic.lean
+++ b/EasyLean/Basic.lean
@@ -1,12 +1,2 @@
-import Mathlib.Data.Real.Basic
-import Mathlib.Tactic.Linarith
-
-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
+import Mathlib
+import EasyLean.Mathd.Algebra.mathd_algebra_513
diff --git a/EasyLean/Mathd/Algebra/mathd_algebra_513.lean b/EasyLean/Mathd/Algebra/mathd_algebra_513.lean
new file mode 100644
index 0000000..976d580
--- /dev/null
+++ b/EasyLean/Mathd/Algebra/mathd_algebra_513.lean
@@ -0,0 +1,8 @@
+import Mathlib
+import EasyLean.Mathd.Algebra.mathd_algebra_513_a
+import EasyLean.Mathd.Algebra.mathd_algebra_513_b
+
+theorem mathd_algebra_513 (a b : ℝ) (h₀ : 3 * a + 2 * b = 5) (h₁ : a + b = 2) : a = 1 ∧ b = 1 := by
+  have ha : a = 1 := mathd_algebra_513_a a b h₀ h₁
+  have hb : b = 1 := mathd_algebra_513_b a b h₁ ha
+  exact ⟨ha, hb⟩
diff --git a/EasyLean/Mathd/Algebra/mathd_algebra_513_a.lean b/EasyLean/Mathd/Algebra/mathd_algebra_513_a.lean
new file mode 100644
index 0000000..a6f2169
--- /dev/null
+++ b/EasyLean/Mathd/Algebra/mathd_algebra_513_a.lean
@@ -0,0 +1,6 @@
+import Mathlib
+
+theorem mathd_algebra_513_a (a b : ℝ) (h0 : 3 * a + 2 * b = 5) (h1 : a + b = 2) : a = 1 := by
+  have : a = 1 := by
+    linear_combination h0 - (2 : ℝ) * h1
+  exact this
diff --git a/EasyLean/Mathd/Algebra/mathd_algebra_513_b.lean b/EasyLean/Mathd/Algebra/mathd_algebra_513_b.lean
new file mode 100644
index 0000000..33ca240
--- /dev/null
+++ b/EasyLean/Mathd/Algebra/mathd_algebra_513_b.lean
@@ -0,0 +1,6 @@
+import Mathlib
+
+theorem mathd_algebra_513_b (a b : ℝ) (h1 : a + b = 2) (ha : a = 1) : b = 1 := by
+  have hb' : 1 + b = 2 := by simpa [ha] using h1
+  have hb'' : b = 1 := by linarith [hb']
+  exact hb''