diff --git a/solver/src/reasoners/eq/mod.rs b/solver/src/reasoners/eq/mod.rs
index 86506206..730fc05d 100644
--- a/solver/src/reasoners/eq/mod.rs
+++ b/solver/src/reasoners/eq/mod.rs
@@ -2,12 +2,13 @@ use crate::backtrack::{Backtrack, DecLvl, EventIndex, ObsTrailCursor, Trail};
 use crate::collections::ref_store::RefMap;
 use crate::core::literals::Watches;
 use crate::core::state::{Cause, Domains, Explanation, InvalidUpdate};
-use crate::core::{Lit, VarRef};
+use crate::core::{Lit, SignedVar, VarRef};
 use crate::model::{Label, Model};
 use crate::reasoners::{Contradiction, ReasonerId, Theory};
 use crate::reif::ReifExpr;
 use itertools::Itertools;
 use std::collections::{HashMap, HashSet};
+use std::ops::Shl;
 
 #[derive(Copy, Clone, Debug)]
 struct OutEdge {
@@ -71,7 +72,34 @@ struct DirEdgeLabel {
 
 #[derive(Clone, Debug)]
 enum Event {
-    Propagation { x: VarRef, y: VarRef, z: VarRef },
+    EdgePropagation { x: VarRef, y: VarRef, z: VarRef },
+}
+
+enum InferenceCause {
+    EdgePropagation(EventIndex),
+    UBPropagation { source: SignedVar },
+}
+
+impl From<InferenceCause> for u32 {
+    fn from(value: InferenceCause) -> Self {
+        match value {
+            InferenceCause::EdgePropagation(e) => 0u32 + (u32::from(e) << 1),
+            InferenceCause::UBPropagation { source } => 1u32 + (u32::from(source) << 1),
+        }
+    }
+}
+
+impl From<u32> for InferenceCause {
+    fn from(value: u32) -> Self {
+        let kind = value & 0x1;
+        let payload = value >> 1;
+        match value & 0x1 {
+            0 => InferenceCause::EdgePropagation(EventIndex::from(payload)),
+            1 => InferenceCause::UBPropagation {
+                source: SignedVar::from(payload),
+            },
+        }
+    }
 }
 
 #[derive(Clone, Default)]
@@ -148,7 +176,7 @@ fn set_edge_label(
         Some(true) => Ok(false),
         _ => {
             // there might be a change, record event source to be able to explain it
-            let event = Event::Propagation { x, y, z };
+            let event = Event::EdgePropagation { x, y, z };
             let id = trail.push(event);
             let cause = Cause::inference(ReasonerId::Eq, id);
             domains.set(label, cause)
@@ -312,6 +340,78 @@ impl EqTheory {
         }
         Ok(())
     }
+
+    pub fn propagate_ub_change(&mut self, v: SignedVar, domains: &mut Domains) -> Result<(), InvalidUpdate> {
+        let ub = domains.get_bound(v);
+        let cause = Cause::inference(ReasonerId::Eq, InferenceCause::UBPropagation { source: v });
+
+        for out in &self.graph.succs[v.variable()] {
+            if domains.entails(out.active) {
+                if domains.entails(out.label) {
+                    let svar = if v.is_plus() {
+                        SignedVar::plus(out.succ)
+                    } else {
+                        SignedVar::minus(out.succ)
+                    };
+                    domains.set_bound(svar, ub, cause)?;
+                }
+            }
+        }
+        Ok(())
+    }
+
+    pub fn propagate_eq_domains_lr(
+        &mut self,
+        left: VarRef,
+        right: VarRef,
+        domains: &mut Domains,
+    ) -> Result<(), InvalidUpdate> {
+        debug_assert!(domains.entails(self.graph.active(left, right)));
+        debug_assert!(domains.entails(self.graph.label(left, right)));
+
+        // enforce upper bound by capping inverse var
+        let left = SignedVar::plus(left);
+        let right = SignedVar::plus(right);
+        let cause = Cause::inference(ReasonerId::Eq, InferenceCause::UBPropagation { source: left });
+        let ub = domains.get_bound(left);
+        domains.set_bound(right, ub, cause)?;
+
+        // enforce lower bound by capping inverse var
+        let left = -left;
+        let right = -right;
+        let cause = Cause::inference(ReasonerId::Eq, InferenceCause::UBPropagation { source: left });
+        let ub = domains.get_bound(left);
+        domains.set_bound(right, ub, cause)?;
+
+        Ok(())
+    }
+
+    pub fn propagate_neq_domains_lr(
+        &mut self,
+        left: VarRef,
+        right: VarRef,
+        domains: &mut Domains,
+    ) -> Result<(), InvalidUpdate> {
+        debug_assert!(domains.entails(self.graph.active(left, right)));
+        debug_assert!(domains.entails(!self.graph.label(left, right)));
+
+        // enforce upper bound by capping inverse var
+        let left = SignedVar::plus(left);
+        let right = SignedVar::plus(right);
+        let cause = Cause::inference(ReasonerId::Eq, InferenceCause::UBPropagation { source: left });
+        let ub = domains.get_bound(left);
+        domains.set_bound(right, ub, cause)?;
+
+        // enforce lower bound by capping inverse var
+        let left = -left;
+        let right = -right;
+        let cause = Cause::inference(ReasonerId::Eq, InferenceCause::UBPropagation { source: left });
+        let ub = domains.get_bound(left);
+        domains.set_bound(right, ub, cause)?;
+
+        Ok(())
+    }
+
     pub fn add_edge(&mut self, a: VarRef, b: VarRef, model: &mut impl ReifyEq) -> Lit {
         self.graph.add_node(a, model);
         self.graph.add_node(b, model);
@@ -356,7 +456,7 @@ impl Theory for EqTheory {
     fn explain(&mut self, _: Lit, context: u32, domains: &Domains, out_explanation: &mut Explanation) {
         let event_index = EventIndex::from(context);
         let event = self.trail.get_event(event_index);
-        let &Event::Propagation { x, y, z } = event;
+        let &Event::EdgePropagation { x, y, z } = event;
 
         let mut push_causes = |a, b| {
             let ab_act = self.graph.active(a, b);