Add new theorems and proofs

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 EasyLean.Theorems.TwoMulTwoReal
+import EasyLean.Theorems.MathdAlgebra513

EasyLean/Theorems/MathdAlgebra513.lean

@@ -0,0 +1,12 @@
+import Mathlib
+import EasyLean.Theorems.TwoMulTwoReal
+
+theorem mathd_algebra_513 (a b : ℝ) (h₀ : 3 * a + 2 * b = 5) (h₁ : a + b = 2) :
+    a = 1 ∧ b = 1 := by
+  have h₂ : 2 * a + 2 * b = 2 * 2 := by
+    simpa [mul_add] using congrArg (fun t : ℝ => 2 * t) h₁
+  have ha : a = 1 := by
+    linarith [h₀, h₂]
+  have hb : b = 1 := by
+    linarith [h₁, ha]
+  exact ⟨ha, hb⟩

EasyLean/Theorems/TwoMulTwoReal.lean

@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem two_mul_two_real : (2 : ℝ) * 2 = (4 : ℝ) := by
+  norm_num

Main.lean

@@ -0,0 +1,3 @@
+import EasyLean.Theorems.MathdAlgebra513
+
+def main : IO Unit := pure ()