diff --git a/src/nlsat/levelwise.h b/src/nlsat/levelwise.h
new file mode 100644
index 000000000..9efd8d3a4
--- /dev/null
+++ b/src/nlsat/levelwise.h
@@ -0,0 +1,82 @@
+  // Context for property propagation (e.g., which case of rule 4.2 applies)
+  enum class property_mapping_case : unsigned {
+    case1 = 0, 
+    case2 = 1,  
+    case3 = 3,
+  };
+
+/*++
+  Copyright (c) 2025
+
+  Module Name:
+    levelwise.h
+
+  Abstract:
+    Levelwise algorithm property and mapping definitions (see levelwise paper).
+
+  --*/
+#pragma once
+
+#include <vector>
+#include "nlsat_types.h"
+
+namespace nlsat {
+
+    /**
+     * Properties for indexed roots, in the order specified by the levelwise paper.
+     * The order is important for the algorithm and must match the paper exactly.
+     */
+  enum class polynom_property : unsigned {
+    ir_ord,              // ir_ord(≼, s) for all ≼ for roots of level i and s ∈ Ri−1
+    an_del,              // an_del(p) for all p of level i
+    non_null,            // non_null(p) for all p of level i
+    ord_inv_reducible,   // ord_inv(p) for all reducible p of level i
+    ord_inv_irreducible, // ord_inv(p) for all irreducible p of level i
+    sgn_inv_reducible,   // sgn_inv(p) for all reducible p of level i
+    sgn_inv_irreducible, // sgn_inv(p) for all irreducible p of level i
+    connected,           // connected(i)
+    an_sub,              // an_sub(i)
+    sample,              // sample(s) for all s ∈ Ri of level i
+    repr,                // repr(I, s) for all I of level i and s ∈ ...
+    _count               // always last: number of properties
+  };
+
+    // Utility: property to string (for debugging, logging, etc.)
+  inline const char* to_string(polynom_property prop) {
+    switch (prop) {
+    case polynom_property::ir_ord:              return "ir_ord";
+    case polynom_property::an_del:              return "an_del";
+    case polynom_property::non_null:            return "non_null";
+    case polynom_property::ord_inv_reducible:   return "ord_inv_reducible";
+    case polynom_property::ord_inv_irreducible: return "ord_inv_irreducible";
+    case polynom_property::sgn_inv_reducible:   return "sgn_inv_reducible";
+    case polynom_property::sgn_inv_irreducible: return "sgn_inv_irreducible";
+    case polynom_property::connected:           return "connected";
+    case polynom_property::an_sub:              return "an_sub";
+    case polynom_property::sample:              return "sample";
+    case polynom_property::repr:                return "repr";
+    default: return "unknown";
+    }
+  }
+
+
+  // Property propagation mapping: for each property, the set of properties it implies (see levelwise paper, e.g., rule 4.2)
+  // Example: property_dependencies[root_property::sgn_inv] = {root_property::ord_inv, ...}
+  // Overload: property_dependencies with context (for rules like 4.2 with multiple cases)
+  inline const std::vector<polynom_property>& property_dependencies(polynom_property prop, property_mapping_case p_case) {
+    // Each property has a table of vectors, one per context case
+    static const std::vector<polynom_property> table[][2] = {
+      /* sgn_inv  */ { { /* case1: ... */ }, { /* case2: ... */ } },
+      /* ord_inv  */ { { /* case1: ... */ }, { /* case2: ... */ } },
+      /* non_null */ { { /* case1: ... */ }, { /* case2: ... */ } }
+      // Extend as needed for more properties
+    };
+    return table[(unsigned)prop][(unsigned)p_case];
+  }
+
+  // For static (context-free) queries, default to case1
+  inline const std::vector<polynom_property>& property_dependencies(polynom_property prop) {
+    return property_dependencies(prop, property_mapping_case::case1);
+  }
+
+} // namespace nlsat
diff --git a/src/nlsat/nlsat_explain.cpp b/src/nlsat/nlsat_explain.cpp
index 83c5f31b6..492834bdc 100644
--- a/src/nlsat/nlsat_explain.cpp
+++ b/src/nlsat/nlsat_explain.cpp
@@ -17,6 +17,7 @@ Revision History:
 
 --*/
 #include "nlsat/nlsat_explain.h"
+#include "nlsat/levelwise.h"
 #include "nlsat/nlsat_assignment.h"
 #include "nlsat/nlsat_evaluator.h"
 #include "math/polynomial/algebraic_numbers.h"