diff --git a/app-proto/src/assembly.rs b/app-proto/src/assembly.rs
index 8217922..6c4aeb7 100644
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@@ -7,13 +7,17 @@ use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 
 use crate::engine::{realize_gram, PartialMatrix};
 
+// the types of the keys we use to access an assembly's elements and constraints
+pub type ElementKey = usize;
+pub type ConstraintKey = usize;
+
 #[derive(Clone, PartialEq)]
 pub struct Element {
     pub id: String,
     pub label: String,
     pub color: [f32; 3],
     pub representation: DVector<f64>,
-    pub constraints: BTreeSet<usize>,
+    pub constraints: BTreeSet<ConstraintKey>,
     
     // internal properties, not reflected in any view
     pub index: usize
@@ -21,7 +25,7 @@ pub struct Element {
 
 #[derive(Clone)]
 pub struct Constraint {
-    pub subjects: (usize, usize),
+    pub subjects: (ElementKey, ElementKey),
     pub rep: Signal<f64>,
     pub rep_text: Signal<String>,
     pub rep_valid: Signal<bool>,
@@ -36,7 +40,7 @@ pub struct Assembly {
     pub constraints: Signal<Slab<Constraint>>,
     
     // indexing
-    pub elements_by_id: Signal<FxHashMap<String, usize>>
+    pub elements_by_id: Signal<FxHashMap<String, ElementKey>>
 }
 
 impl Assembly {
diff --git a/app-proto/src/main.rs b/app-proto/src/main.rs
index 2c71a83..897f9d4 100644
--- a/app-proto/src/main.rs
+++ b/app-proto/src/main.rs
@@ -8,14 +8,14 @@ use rustc_hash::FxHashSet;
 use sycamore::prelude::*;
 
 use add_remove::AddRemove;
-use assembly::Assembly;
+use assembly::{Assembly, ElementKey};
 use display::Display;
 use outline::Outline;
 
 #[derive(Clone)]
 struct AppState {
     assembly: Assembly,
-    selection: Signal<FxHashSet<usize>>
+    selection: Signal<FxHashSet<ElementKey>>
 }
 
 impl AppState {
diff --git a/app-proto/src/outline.rs b/app-proto/src/outline.rs
index 98b422f..0a8816d 100644
--- a/app-proto/src/outline.rs
+++ b/app-proto/src/outline.rs
@@ -150,7 +150,7 @@ pub fn Outline() -> View {
                                 ul(class="constraints") {
                                     Keyed(
                                         list=elt.constraints.into_iter().collect::<Vec<_>>(),
-                                        view=move |c_key: usize| {
+                                        view=move |c_key| {
                                             let c_state = use_context::<AppState>();
                                             let assembly = &c_state.assembly;
                                             let cst = assembly.constraints.with(|csts| csts[c_key].clone());