diff --git a/patronus-egraphs/src/lib.rs b/patronus-egraphs/src/lib.rs
index 01141d0..81897b1 100644
--- a/patronus-egraphs/src/lib.rs
+++ b/patronus-egraphs/src/lib.rs
@@ -7,4 +7,4 @@ mod rewrites;
 pub use arithmetic::{
     from_arith, get_const_width_or_sign, is_bin_op, to_arith, Arith, EGraph, Sign,
 };
-pub use rewrites::{create_egg_rewrites, create_rewrites, ArithRewrite};
+pub use rewrites::{create_egg_rewrites, create_rewrites, ArithRewrite, Assignment};
diff --git a/patronus-egraphs/src/rewrites.rs b/patronus-egraphs/src/rewrites.rs
index 7022016..0d2cdd3 100644
--- a/patronus-egraphs/src/rewrites.rs
+++ b/patronus-egraphs/src/rewrites.rs
@@ -10,7 +10,10 @@ introspect them in order to check re-write conditions or debug matches.
 !*/
 
 use crate::{get_const_width_or_sign, is_bin_op, Arith, EGraph};
-use egg::{ConditionalApplier, ENodeOrVar, Language, Pattern, PatternAst, Rewrite, Subst, Var};
+use egg::{
+    ConditionalApplier, ENodeOrVar, Id, Language, Pattern, PatternAst, Rewrite, Searcher, Subst,
+    Var,
+};
 use patronus::expr::WidthInt;
 use std::cmp::max;
 
@@ -159,6 +162,54 @@ impl ArithRewrite {
             true
         }
     }
+
+    pub fn find_lhs_matches(&self, egraph: &EGraph) -> Vec<ArithMatch> {
+        self.lhs
+            .search(egraph)
+            .into_iter()
+            .flat_map(|m| {
+                let eclass = m.eclass;
+                m.substs.into_iter().map(move |s| {
+                    let assign = substitution_to_assignment(egraph, &s, &self.lhs.ast);
+                    let cond_res = self.eval_condition(&assign);
+                    ArithMatch {
+                        eclass,
+                        assign,
+                        cond_res,
+                    }
+                })
+            })
+            .collect()
+    }
+}
+
+fn substitution_to_assignment(
+    egraph: &EGraph,
+    s: &Subst,
+    pattern: &PatternAst<Arith>,
+) -> Assignment {
+    vars_in_pattern(pattern)
+        .flat_map(|v| match get_const_width_or_sign(egraph, s[v]) {
+            Some(w) => Some((v, w)),
+            None => None,
+        })
+        .collect()
+}
+
+fn vars_in_pattern(pattern: &PatternAst<Arith>) -> impl Iterator<Item = Var> + '_ {
+    pattern.as_ref().iter().flat_map(|e| match e {
+        ENodeOrVar::Var(v) => Some(*v),
+        ENodeOrVar::ENode(_) => None,
+    })
+}
+
+pub type Assignment = Vec<(Var, WidthInt)>;
+
+#[derive(Debug, Clone)]
+pub struct ArithMatch {
+    eclass: Id,
+    assign: Assignment,
+    cond_res: bool,
 }
 
 /// Checks that input and output widths of operations are consistent.
@@ -222,7 +273,6 @@ mod tests {
     use super::*;
     use crate::arithmetic::verification_fig_1;
     use crate::to_arith;
-    use egg::Searcher;
     use patronus::expr::{Context, SerializableIrNode};
     #[test]
     fn test_data_path_verification_fig_1_rewrites() {
@@ -247,11 +297,11 @@ mod tests {
         let impl_class = runner.roots[1];
         println!("{spec_class} {impl_class}");
 
-        let pat: Pattern<Arith> =
-            "(<< ?wo ?wab unsign (* ?wab ?wa unsign ?a ?wb unsign ?b) ?wc unsign ?c)"
-                .parse()
-                .unwrap();
-        let r = pat.search(&runner.egraph);
+        let left_shift_mult = create_rewrites()
+            .into_iter()
+            .find(|r| r.name == "left-shift-mult")
+            .unwrap();
+        let r = left_shift_mult.find_lhs_matches(&runner.egraph);
         for m in r {
             println!("{m:?}");
         }
diff --git a/tools/egraphs-cond-synth/src/samples.rs b/tools/egraphs-cond-synth/src/samples.rs
index cb99b73..3fbc7c5 100644
--- a/tools/egraphs-cond-synth/src/samples.rs
+++ b/tools/egraphs-cond-synth/src/samples.rs
@@ -321,8 +321,6 @@ pub struct RuleSymbol {
     sign: VarOrConst,
 }
 
-pub type Assignment = Vec<(Var, WidthInt)>;
-
 impl RuleInfo {
     pub fn signs(&self) -> impl Iterator<Item = Var> + '_ {
         self.signs.iter().cloned()