diff --git a/Cargo.toml b/Cargo.toml
index 9a9a531db29..c996600fb14 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -23,6 +23,8 @@ lexical-core = { version = "0.8", optional = true }
 # We need to Hash values before sending them to an hasher. This
 # crate provides HashMap that assumes pre-hashed values.
 hash_hasher = "^2.0.3"
+# For SIMD utf8 validation
+simdutf8 = "0.1.3"
 
 csv = { version = "^1.1", optional = true }
 regex = { version = "^1.3", optional = true }
@@ -68,15 +70,13 @@ strength_reduce = { version = "0.2", optional = true }
 # For instruction multiversioning
 multiversion = { version = "0.6.1", optional = true }
 
-# For SIMD utf8 validation
-simdutf8 = "0.1.3"
-
 [dev-dependencies]
-rand = "0.8"
 criterion = "0.3"
 flate2 = "1"
 doc-comment = "0.3"
 crossbeam-channel = "0.5.1"
+# used to run formal property testing
+proptest = { version = "1", default_features = false, features = ["std"] }
 
 [package.metadata.docs.rs]
 features = ["full"]
diff --git a/tests/it/array/binary/mutable.rs b/tests/it/array/binary/mutable.rs
index c42431b15ee..6763a9d4984 100644
--- a/tests/it/array/binary/mutable.rs
+++ b/tests/it/array/binary/mutable.rs
@@ -1,4 +1,4 @@
-use arrow2::array::{Array, BinaryArray, MutableBinaryArray};
+use arrow2::array::{BinaryArray, MutableBinaryArray};
 use arrow2::bitmap::Bitmap;
 
 #[test]
diff --git a/tests/it/array/utf8/mutable.rs b/tests/it/array/utf8/mutable.rs
index 20087010743..cde2a9eeafe 100644
--- a/tests/it/array/utf8/mutable.rs
+++ b/tests/it/array/utf8/mutable.rs
@@ -1,4 +1,4 @@
-use arrow2::array::{Array, MutableUtf8Array, Utf8Array};
+use arrow2::array::{MutableUtf8Array, Utf8Array};
 use arrow2::bitmap::Bitmap;
 use arrow2::buffer::MutableBuffer;
 use arrow2::datatypes::DataType;
diff --git a/tests/it/bitmap/bitmap_ops.rs b/tests/it/bitmap/bitmap_ops.rs
index 12080438761..18eda8e3ab9 100644
--- a/tests/it/bitmap/bitmap_ops.rs
+++ b/tests/it/bitmap/bitmap_ops.rs
@@ -1,12 +1,16 @@
+use proptest::prelude::*;
+
 use arrow2::bitmap::Bitmap;
 
-#[test]
-fn not_random() {
-    let iter = (0..100).map(|x| x % 7 == 0);
-    let iter_not = iter.clone().map(|x| !x);
+use crate::bitmap::bitmap_strategy;
 
-    let bitmap: Bitmap = iter.collect();
-    let expected: Bitmap = iter_not.collect();
+proptest! {
+    /// Asserts that !bitmap equals all bits flipped
+    #[test]
+    #[cfg_attr(miri, ignore)] // miri and proptest do not work well :(
+    fn not(bitmap in bitmap_strategy()) {
+        let not_bitmap: Bitmap = bitmap.iter().map(|x| !x).collect();
 
-    assert_eq!(!&bitmap, expected);
+        assert_eq!(!&bitmap, not_bitmap);
+    }
 }
diff --git a/tests/it/bitmap/mod.rs b/tests/it/bitmap/mod.rs
index 78d47d604d3..3b415d0a6c2 100644
--- a/tests/it/bitmap/mod.rs
+++ b/tests/it/bitmap/mod.rs
@@ -3,8 +3,28 @@ mod immutable;
 mod mutable;
 mod utils;
 
+use proptest::prelude::*;
+
 use arrow2::{bitmap::Bitmap, buffer::MutableBuffer};
 
+/// Returns a strategy of an arbitrary sliced [`Bitmap`] of size up to 1000
+pub(crate) fn bitmap_strategy() -> impl Strategy<Value = Bitmap> {
+    prop::collection::vec(any::<bool>(), 1..1000)
+        .prop_flat_map(|vec| {
+            let len = vec.len();
+            (Just(vec), 0..len)
+        })
+        .prop_flat_map(|(vec, index)| {
+            let len = vec.len();
+            (Just(vec), Just(index), 0..len - index)
+        })
+        .prop_flat_map(|(vec, index, len)| {
+            let bitmap = Bitmap::from(&vec);
+            let bitmap = bitmap.slice(index, len);
+            Just(bitmap)
+        })
+}
+
 fn create_bitmap<P: AsRef<[u8]>>(bytes: P, len: usize) -> Bitmap {
     let buffer = MutableBuffer::<u8>::from(bytes.as_ref());
     Bitmap::from_u8_buffer(buffer, len)
diff --git a/tests/it/bitmap/utils/mod.rs b/tests/it/bitmap/utils/mod.rs
index 4392ca4510c..e92f31124ca 100644
--- a/tests/it/bitmap/utils/mod.rs
+++ b/tests/it/bitmap/utils/mod.rs
@@ -1,5 +1,9 @@
+use proptest::prelude::*;
+
 use arrow2::bitmap::utils::*;
 
+use crate::bitmap::bitmap_strategy;
+
 mod bit_chunks_exact;
 mod chunk_iter;
 mod iterator;
@@ -67,3 +71,13 @@ fn count_zeros_1() {
     let input: &[u8] = &[73, 146, 36, 73, 146, 36, 73, 146, 36, 73, 146, 36, 9];
     assert_eq!(count_zeros(input, 10, 90), 60);
 }
+
+proptest! {
+    /// Asserts that `Bitmap::null_count` equals the number of unset bits
+    #[test]
+    #[cfg_attr(miri, ignore)] // miri and proptest do not work well :(
+    fn null_count(bitmap in bitmap_strategy()) {
+        let sum_of_sets: usize = (0..bitmap.len()).map(|x| (!bitmap.get_bit(x)) as usize).sum();
+        assert_eq!(bitmap.null_count(), sum_of_sets);
+    }
+}
diff --git a/tests/it/bitmap/utils/slice_iterator.rs b/tests/it/bitmap/utils/slice_iterator.rs
index ea60940c41f..f9d9e409cec 100644
--- a/tests/it/bitmap/utils/slice_iterator.rs
+++ b/tests/it/bitmap/utils/slice_iterator.rs
@@ -1,27 +1,34 @@
-use rand::distributions::{Bernoulli, Uniform};
-use rand::prelude::StdRng;
-use rand::Rng;
-use rand::SeedableRng;
+use proptest::prelude::*;
 
 use arrow2::bitmap::utils::SlicesIterator;
 use arrow2::bitmap::Bitmap;
 
-#[test]
-fn check_invariant() {
-    let values = (0..8).map(|i| i % 2 != 0).collect::<Bitmap>();
-    let iter = SlicesIterator::new(&values);
+use crate::bitmap::bitmap_strategy;
 
-    let slots = iter.slots();
+proptest! {
+    /// Asserts that:
+    /// * `slots` is the number of set bits in the bitmap
+    /// * the sum of the lens of the slices equals `slots`
+    /// * each item on each slice is set
+    #[test]
+    #[cfg_attr(miri, ignore)] // miri and proptest do not work well :(
+    fn check_invariants(bitmap in bitmap_strategy()) {
+        let iter = SlicesIterator::new(&bitmap);
 
-    let slices = iter.collect::<Vec<_>>();
+        let slots = iter.slots();
 
-    assert_eq!(slices, vec![(1, 1), (3, 1), (5, 1), (7, 1)]);
+        assert_eq!(bitmap.len() - bitmap.null_count(), slots);
 
-    let mut sum = 0;
-    for (_, len) in slices {
-        sum += len;
+        let slices = iter.collect::<Vec<_>>();
+        let mut sum = 0;
+        for (start, len) in slices {
+            sum += len;
+            for i in start..(start+len) {
+                assert!(bitmap.get_bit(i));
+            }
+        }
+        assert_eq!(sum, slots);
     }
-    assert_eq!(sum, slots);
 }
 
 #[test]
@@ -142,28 +149,3 @@ fn remainder_1() {
     let chunks = iter.collect::<Vec<_>>();
     assert_eq!(chunks, vec![(2, 1), (4, 1)]);
 }
-
-#[test]
-fn filter_slices() {
-    let mut rng = StdRng::seed_from_u64(42);
-    let length = 500;
-
-    let mask: Bitmap = (0..length)
-        .map(|_| {
-            let v: bool = (&mut rng).sample(Bernoulli::new(0.5).unwrap());
-            v
-        })
-        .collect();
-
-    for offset in 100usize..(length - 1) {
-        let len = (&mut rng).sample(Uniform::new(0, length - offset));
-        let mask_s = mask.clone().slice(offset, len);
-
-        let iter = SlicesIterator::new(&mask_s);
-        iter.for_each(|(start, slice_len)| {
-            if start + slice_len > len {
-                panic!("Fail")
-            }
-        });
-    }
-}