diff --git a/Algorithm/Data/Classes/ToList.lean b/Algorithm/Data/Classes/ToList.lean
index c4312a4..c556004 100644
--- a/Algorithm/Data/Classes/ToList.lean
+++ b/Algorithm/Data/Classes/ToList.lean
@@ -23,7 +23,7 @@ lemma head?_isSome' : (head? l).isSome = !l.isEmpty :=
 lemma tail?_isSome' : (tail? l).isSome = !l.isEmpty :=
   match l with | [] | _ :: _ => rfl
 
-lemma isEmpty_eq_decide_eq_nil [DecidableEq α] : l.isEmpty = decide (l = []) := by
+lemma isEmpty_eq_decide_eq_nil : l.isEmpty = decide (l = []) := by
   cases l <;> simp [isEmpty]
 
 lemma isEmpty_eq_decide_length : l.isEmpty = decide (l.length = 0) := by
diff --git a/docbuild/lakefile.toml b/docbuild/lakefile.toml
index 26784eb..7f02734 100644
--- a/docbuild/lakefile.toml
+++ b/docbuild/lakefile.toml
@@ -10,4 +10,4 @@ path = "../"
 [[require]]
 scope = "leanprover"
 name = "doc-gen4"
-rev = "v4.26.0"
+rev = "v4.27.0-rc1"
diff --git a/lake-manifest.json b/lake-manifest.json
index c2c7d5f..441cfee 100644
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -5,17 +5,17 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "2df2f0150c275ad53cb3c90f7c98ec15a56a1a67",
+   "rev": "32d24245c7a12ded17325299fd41d412022cd3fe",
    "name": "mathlib",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v4.26.0",
+   "inputRev": "v4.27.0-rc1",
    "inherited": false,
    "configFile": "lakefile.lean"},
   {"url": "https://github.com/leanprover-community/plausible",
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "160af9e8e7d4ae448f3c92edcc5b6a8522453f11",
+   "rev": "8d3713f36dda48467eb61f8c1c4db89c49a6251a",
    "name": "plausible",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -25,7 +25,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "3591c3f664ac3719c4c86e4483e21e228707bfa2",
+   "rev": "19e5f5cc9c21199be466ef99489e3acab370f079",
    "name": "LeanSearchClient",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -35,7 +35,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "e9f31324f15ead11048b1443e62c5deaddd055d2",
+   "rev": "4eb26e1a4806b200ddfe5179d0c2a0fae56c54a7",
    "name": "importGraph",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -45,17 +45,17 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "b4fb2aa5290ebf61bc5f80a5375ba642f0a49192",
+   "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
    "name": "proofwidgets",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v0.0.83",
+   "inputRev": "v0.0.84",
    "inherited": true,
    "configFile": "lakefile.lean"},
   {"url": "https://github.com/leanprover-community/aesop",
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "2f6d238744c4cb07fdc91240feaf5d4221a27931",
+   "rev": "fb12f5535c80e40119286d9575c9393562252d21",
    "name": "aesop",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -65,7 +65,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "9312503909aa8e8bb392530145cc1677a6298574",
+   "rev": "523ec6fc8062d2f470fdc8de6f822fe89552b5e6",
    "name": "Qq",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -75,7 +75,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "24241822ef9d3e7f6a3bcc53ad136e12663db8f3",
+   "rev": "6254bed25866358ce4f841fa5a13b77de04ffbc8",
    "name": "batteries",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -85,10 +85,10 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover",
-   "rev": "933fce7e893f65969714c60cdb4bd8376786044e",
+   "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
    "name": "Cli",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v4.26.0",
+   "inputRev": "v4.27.0-rc1",
    "inherited": true,
    "configFile": "lakefile.toml"}],
  "name": "algorithm",
diff --git a/lakefile.lean b/lakefile.lean
index a164bde..a8a0424 100644
--- a/lakefile.lean
+++ b/lakefile.lean
@@ -2,7 +2,7 @@ import Lake
 
 open Lake DSL
 
-require "leanprover-community" / "mathlib" @ git "v4.26.0"
+require "leanprover-community" / "mathlib" @ git "v4.27.0-rc1"
 
 abbrev algorithmOnlyLinters : Array LeanOption := #[
   ⟨`linter.mathlibStandardSet, true⟩,
diff --git a/lean-toolchain b/lean-toolchain
index e59446d..bd19bde 100644
--- a/lean-toolchain
+++ b/lean-toolchain
@@ -1 +1 @@
-leanprover/lean4:v4.26.0
+leanprover/lean4:v4.27.0-rc1