diff --git a/library/core/src/iter/range.rs b/library/core/src/iter/range.rs
index 68937161e046a..2ecf9ce5b81b3 100644
--- a/library/core/src/iter/range.rs
+++ b/library/core/src/iter/range.rs
@@ -22,7 +22,7 @@ unsafe_impl_trusted_step![AsciiChar char i8 i16 i32 i64 i128 isize u8 u16 u32 u6
 ///
 /// The *successor* operation moves towards values that compare greater.
 /// The *predecessor* operation moves towards values that compare lesser.
-#[unstable(feature = "step_trait", reason = "recently redesigned", issue = "42168")]
+#[unstable(feature = "step_trait", issue = "42168")]
 pub trait Step: Clone + PartialOrd + Sized {
     /// Returns the number of *successor* steps required to get from `start` to `end`.
     ///
@@ -52,15 +52,12 @@ pub trait Step: Clone + PartialOrd + Sized {
     /// For any `a`, `n`, and `m`:
     ///
     /// * `Step::forward_checked(a, n).and_then(|x| Step::forward_checked(x, m)) == Step::forward_checked(a, m).and_then(|x| Step::forward_checked(x, n))`
-    ///
-    /// For any `a`, `n`, and `m` where `n + m` does not overflow:
-    ///
-    /// * `Step::forward_checked(a, n).and_then(|x| Step::forward_checked(x, m)) == Step::forward_checked(a, n + m)`
+    /// * `Step::forward_checked(a, n).and_then(|x| Step::forward_checked(x, m)) == try { Step::forward_checked(a, n.checked_add(m)) }`
     ///
     /// For any `a` and `n`:
     ///
     /// * `Step::forward_checked(a, n) == (0..n).try_fold(a, |x, _| Step::forward_checked(&x, 1))`
-    ///   * Corollary: `Step::forward_checked(&a, 0) == Some(a)`
+    ///   * Corollary: `Step::forward_checked(a, 0) == Some(a)`
     fn forward_checked(start: Self, count: usize) -> Option<Self>;
 
     /// Returns the value that would be obtained by taking the *successor*
@@ -106,6 +103,7 @@ pub trait Step: Clone + PartialOrd + Sized {
     /// * if there exists `b` such that `b > a`, it is safe to call `Step::forward_unchecked(a, 1)`
     /// * if there exists `b`, `n` such that `steps_between(&a, &b) == Some(n)`,
     ///   it is safe to call `Step::forward_unchecked(a, m)` for any `m <= n`.
+    ///   * Corollary: `Step::forward_unchecked(a, 0)` is always safe.
     ///
     /// For any `a` and `n`, where no overflow occurs:
     ///
@@ -128,8 +126,8 @@ pub trait Step: Clone + PartialOrd + Sized {
     ///
     /// For any `a` and `n`:
     ///
-    /// * `Step::backward_checked(a, n) == (0..n).try_fold(a, |x, _| Step::backward_checked(&x, 1))`
-    ///   * Corollary: `Step::backward_checked(&a, 0) == Some(a)`
+    /// * `Step::backward_checked(a, n) == (0..n).try_fold(a, |x, _| Step::backward_checked(x, 1))`
+    ///   * Corollary: `Step::backward_checked(a, 0) == Some(a)`
     fn backward_checked(start: Self, count: usize) -> Option<Self>;
 
     /// Returns the value that would be obtained by taking the *predecessor*
@@ -175,6 +173,7 @@ pub trait Step: Clone + PartialOrd + Sized {
     /// * if there exists `b` such that `b < a`, it is safe to call `Step::backward_unchecked(a, 1)`
     /// * if there exists `b`, `n` such that `steps_between(&b, &a) == Some(n)`,
     ///   it is safe to call `Step::backward_unchecked(a, m)` for any `m <= n`.
+    ///   * Corollary: `Step::backward_unchecked(a, 0)` is always safe.
     ///
     /// For any `a` and `n`, where no overflow occurs:
     ///