Switch update lock files to cargo-rbmt

diff --git a/contrib/update-lock-files.sh b/contrib/update-lock-files.sh
deleted file mode 100755
index 6d73aae9..00000000
--- a/contrib/update-lock-files.sh
+++ /dev/null
@@ -1,30 +0,0 @@
-#!/usr/bin/env bash
-#
-# Update the minimal and recent lock files.
-
-set -euo pipefail
-
-NIGHTLY=$(cat nightly-version)
-
-# The `direct-minimal-versions` and `minimal-versions` dependency
-# resolution strategy flags each have a little quirk. `direct-minimal-versions`
-# allows transitive versions to upgrade, so we are not testing against
-# the actual minimum tree. `minimal-versions` allows the direct dependency
-# versions to resolve upward due to transitive requirements, so we are
-# not testing the manifest's versions. Combo'd together though, we
-# can get the best of both worlds to ensure the actual minimum dependencies
-# listed in the crate manifests build.
-
-# Check that all explicit direct dependency versions are not lying,
-# as in, they are not being bumped up by transitive dependency constraints.
-rm -f Cargo.lock && cargo +"$NIGHTLY" check --all-features -Z direct-minimal-versions
-# Now that our own direct dependency versions can be trusted, check
-# against the lowest versions of the dependency tree which still
-# satisfy constraints. Use this as the minimal version lock file.
-rm -f Cargo.lock && cargo +"$NIGHTLY" check --all-features -Z minimal-versions
-cp -f Cargo.lock Cargo-minimal.lock
-
-# Conservatively bump of recent dependencies.
-cp -f Cargo-recent.lock Cargo.lock
-cargo check --all-features
-cp -f Cargo.lock Cargo-recent.lock
diff --git a/justfile b/justfile
index 9e2cf336..051f7abf 100644
--- a/justfile
+++ b/justfile
@@ -8,10 +8,13 @@ alias ulf := update-lock-files
 _default:
   @just --list
 
+# Install necessary dev tools on system.
+_install-tools:
+  @{{justfile_directory()}}/contrib/ensure-maintainer-tools.sh
+
 # Run the given CI task using maintainer tools.
 [group('ci')]
-@ci task toolchain="stable" lock="recent":
-  {{justfile_directory()}}/contrib/ensure-maintainer-tools.sh
+@ci task toolchain="stable" lock="recent": _install-tools
   RBMT_LOG_LEVEL=quiet cargo +{{toolchain}} rbmt {{task}} --lock-file {{lock}}
 
 # Test workspace with stable toolchain.
@@ -63,8 +66,8 @@ check-api:
 
 # Update the recent and minimal lock files.
 [group('scripts')]
-update-lock-files:
- {{justfile_directory()}}/contrib/update-lock-files.sh
+@update-lock-files: _install-tools
+  cargo +{{NIGHTLY_VERSION}} rbmt lock
 
 # Install githooks.
 [group('scripts')]