diff --git a/src/main/scala/quickcheck/QuickCheck.scala b/src/main/scala/quickcheck/QuickCheck.scala
index 59ca28b..32fd1af 100644
--- a/src/main/scala/quickcheck/QuickCheck.scala
+++ b/src/main/scala/quickcheck/QuickCheck.scala
@@ -7,12 +7,60 @@ import Prop.{BooleanOperators => _, _}
 
 abstract class QuickCheckHeap extends Properties("Heap") with IntHeap {
 
-  lazy val genHeap: Gen[H] = ???
+  lazy val genHeap: Gen[H] = for {
+    a <- arbitrary[Int]
+    h <- oneOf(const(empty), genHeap)
+  } yield insert(a, h)
+
   implicit lazy val arbHeap: Arbitrary[H] = Arbitrary(genHeap)
 
+  property("min1") = forAll { (a: Int) =>
+    val h = insert(a, empty)
+    findMin(h) == a
+  }
+
   property("gen1") = forAll { (h: H) =>
     val m = if isEmpty(h) then 0 else findMin(h)
     findMin(insert(m, h)) == m
   }
 
+  property("smallest") = forAll { (a: Int, b: Int) =>
+    val h = insert(b, insert(a, empty))
+    val min = if (a<b) then a else b
+    if (a==b) true else
+      findMin(h) == min
+  }
+
+  property("deleteSingle") = forAll { (a: Int) =>
+    val h = insert(a, empty)
+    val h1 = deleteMin(h)
+    isEmpty(h1)
+  }
+
+  def multiMins(h: H, l: List[Int]): List[Int] = {
+    if (isEmpty(h)) then l
+    else findMin(h) :: multiMins(deleteMin(h), l)
+  }
+
+  property("multiMins") = forAll { (h1: H) =>
+    val xs = multiMins(h1, Nil)
+    xs == xs.sorted
+  }
+
+  property("meldMin") = forAll { (h1: H, h2: H) =>
+    val min1 = findMin(h1)
+    val min2 = findMin(h2)
+    val m = meld(h1, h2)
+    val minMeld = findMin(m)
+    minMeld == min1 || minMeld == min2
+  }
+
+  property("meldMinMove") = forAll { (h1: H, h2: H) =>
+    val meld1 = meld(h1, h2)
+    val min1 = findMin(h1)
+    val meld2 = meld(deleteMin(h1), insert(min1, h2))
+    val xs1 = multiMins(meld1, Nil)
+    val xs2 = multiMins(meld2, Nil)
+    xs1 == xs2
+  }
 }