diff --git a/doc/flake.nix b/doc/flake.nix
index 2d03ca3f0f3..88dd52ada7f 100644
--- a/doc/flake.nix
+++ b/doc/flake.nix
@@ -27,7 +27,7 @@
         src = inputs.mdBook;
         cargoDeps = drv.cargoDeps.overrideAttrs (_: {
           inherit src;
-          outputHash = "sha256-5cAV8tOU3R1cPubseetURDQOzKyoo4485wD5IgeJUhQ=";
+          outputHash = "sha256-mhTWHs/bsmm3FH59SkUxBTl5lEH2Rlz/aF9CuBTu1TE=";
         });
         doCheck = false;
       });
diff --git a/flake.lock b/flake.lock
index 18c6d0b34cc..7662de63765 100644
--- a/flake.lock
+++ b/flake.lock
@@ -2,11 +2,11 @@
   "nodes": {
     "flake-utils": {
       "locked": {
-        "lastModified": 1653893745,
-        "narHash": "sha256-0jntwV3Z8//YwuOjzhV2sgJJPt+HY6KhU7VZUL0fKZQ=",
+        "lastModified": 1656928814,
+        "narHash": "sha256-RIFfgBuKz6Hp89yRr7+NR5tzIAbn52h8vT6vXkYjZoM=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "1ed9fb1935d260de5fe1c2f7ee0ebaae17ed2fa1",
+        "rev": "7e2a3b3dfd9af950a856d66b0a7d01e3c18aa249",
         "type": "github"
       },
       "original": {
@@ -33,11 +33,11 @@
     "lean4-mode": {
       "flake": false,
       "locked": {
-        "lastModified": 1654244721,
-        "narHash": "sha256-AVlr4+WGtJR9DGW/RBq+xNBlyrdmy6cg9dayKHGZowI=",
+        "lastModified": 1656864638,
+        "narHash": "sha256-Th+IOKGspSZEXJZMnoP9GqsuVZLt137JfgZg7Q0sHxQ=",
         "owner": "leanprover",
         "repo": "lean4-mode",
-        "rev": "c10def33f603a43f20a4d32d820b61f7ee5dbe5a",
+        "rev": "f23510741b3291d8f9797df9407b1e45d7f22b23",
         "type": "github"
       },
       "original": {
@@ -69,11 +69,11 @@
         "nixpkgs-regression": "nixpkgs-regression"
       },
       "locked": {
-        "lastModified": 1654239108,
-        "narHash": "sha256-0JzuElxLe5DxM+R4tvBYfvQnMGCERZy4KMRf0JYxxS4=",
+        "lastModified": 1657097207,
+        "narHash": "sha256-SmeGmjWM3fEed3kQjqIAO8VpGmkC2sL1aPE7kKpK650=",
         "owner": "NixOS",
         "repo": "nix",
-        "rev": "1dd7253133c4dfd2e7a16ad6fe505442cef38a5b",
+        "rev": "f6316b49a0c37172bca87ede6ea8144d7d89832f",
         "type": "github"
       },
       "original": {
@@ -84,16 +84,16 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1645296114,
-        "narHash": "sha256-y53N7TyIkXsjMpOG7RhvqJFGDacLs9HlyHeSTBioqYU=",
+        "lastModified": 1653988320,
+        "narHash": "sha256-ZaqFFsSDipZ6KVqriwM34T739+KLYJvNmCWzErjAg7c=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "530a53dcbc9437363471167a5e4762c5fcfa34a1",
+        "rev": "2fa57ed190fd6c7c746319444f34b5917666e5c1",
         "type": "github"
       },
       "original": {
         "owner": "NixOS",
-        "ref": "nixos-21.05-small",
+        "ref": "nixos-22.05-small",
         "repo": "nixpkgs",
         "type": "github"
       }
@@ -116,11 +116,11 @@
     },
     "nixpkgs_2": {
       "locked": {
-        "lastModified": 1654126564,
-        "narHash": "sha256-sgDXDKGmUG4h7OPDOHyQggFQ08ZqVzUIPi8351yhugY=",
+        "lastModified": 1657208011,
+        "narHash": "sha256-BlIFwopAykvdy1DYayEkj6ZZdkn+cVgPNX98QVLc0jM=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "f1c9c23aad972787f00f175651e4cb0d7c7fd5ea",
+        "rev": "2770cc0b1e8faa0e20eb2c6aea64c256a706d4f2",
         "type": "github"
       },
       "original": {