From e0df4fa2e77c0020ffa6e9a1bf3716777e1c250f Mon Sep 17 00:00:00 2001
From: "aleph-prover-test[bot]"
 <247855025+aleph-prover-test[bot]@users.noreply.github.com>
Date: Fri, 19 Dec 2025 07:31:48 +0000
Subject: [PATCH] Add new theorems and proofs

Automated commit at 20251219_073147
---
 EasyLean/Basic.lean                      | 14 +++-----------
 EasyLean/Theorems/eq_four.lean           |  6 ++++++
 EasyLean/Theorems/mathd_algebra_513.lean |  6 ++++++
 3 files changed, 15 insertions(+), 11 deletions(-)
 create mode 100644 EasyLean/Theorems/eq_four.lean
 create mode 100644 EasyLean/Theorems/mathd_algebra_513.lean

diff --git a/EasyLean/Basic.lean b/EasyLean/Basic.lean
index 305e1ca..b14fb7c 100644
--- a/EasyLean/Basic.lean
+++ b/EasyLean/Basic.lean
@@ -1,12 +1,4 @@
-import Mathlib.Data.Real.Basic
-import Mathlib.Tactic.Linarith
+import Mathlib
+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
diff --git a/EasyLean/Theorems/eq_four.lean b/EasyLean/Theorems/eq_four.lean
new file mode 100644
index 0000000..faad609
--- /dev/null
+++ b/EasyLean/Theorems/eq_four.lean
@@ -0,0 +1,6 @@
+import Mathlib
+
+theorem eq_four
+    (a b c d : Nat) (h₁ : a = b) (h₂ : a = d) (h₃ : a = c) : c = b := by
+  exact h₃.symm.trans h₁
+
diff --git a/EasyLean/Theorems/mathd_algebra_513.lean b/EasyLean/Theorems/mathd_algebra_513.lean
new file mode 100644
index 0000000..86f0737
--- /dev/null
+++ b/EasyLean/Theorems/mathd_algebra_513.lean
@@ -0,0 +1,6 @@
+import Mathlib
+
+theorem mathd_algebra_513
+    (a b : ℝ) (h₀ : 3 * a + 2 * b = 5) (h₁ : a + b = 2) : a = 1 ∧ b = 1 := by
+  constructor <;> linarith [h₀, h₁]
+