@@ -30,39 +30,21 @@ &self,
         parameters: &CRHGadget::ParametersVar,
         root: &CRHGadget::OutputVar,
         leaf: impl ToBytesGadget<ConstraintF>,
-    ) -> Result<(), SynthesisError> {
-        self.conditionally_check_membership(parameters, root, leaf, &Boolean::Constant(true))
-    }
-
-    pub fn conditionally_check_membership(
-        &self,
-        parameters: &CRHGadget::ParametersVar,
-        root: &CRHGadget::OutputVar,
-        leaf: impl ToBytesGadget<ConstraintF>,
-        should_enforce: &Boolean<ConstraintF>,
-    ) -> Result<(), SynthesisError> {
+    ) -> Result<Boolean<ConstraintF>, SynthesisError> {
         assert_eq!(self.path.len(), P::HEIGHT - 1);
         // Check that the hash of the given leaf matches the leaf hash in the membership
         // proof.
         let leaf_bits = leaf.to_bytes()?;
         let leaf_hash = CRHGadget::evaluate(parameters, &leaf_bits)?;
-        let cs = leaf_hash
-            .cs()
-            .or(root.cs())
-            .or(should_enforce.cs())
-            .unwrap();
+        let cs = leaf_hash.cs().or(root.cs()).unwrap();
 
         // Check if leaf is one of the bottom-most siblings.
         let leaf_is_left = Boolean::new_witness(cs.ns("leaf_is_left"), || {
             Ok(leaf_hash.value()?.eq(&self.path[0].0.value()?))
         })?;
 
-        leaf_hash.conditional_enforce_equal_or(
-            &leaf_is_left,
-            &self.path[0].0,
-            &self.path[0].1,
-            should_enforce,
-        )?;
+        let mut result =
+            leaf_hash.is_eq(&leaf_is_left.select(&self.path[0].0, &self.path[0].1)?)?;
 
         // Check levels between leaf level and root.
         let mut previous_hash = leaf_hash;
@@ -77,12 +59,8 @@ let ns = cs.ns(format!(
                 "enforcing that inner hash is correct at i-th level{}",
                 i
             ));
-            previous_hash.conditional_enforce_equal_or(
-                &previous_is_left,
-                left_hash,
-                right_hash,
-                should_enforce,
-            )?;
+            let equality_cmp = previous_is_left.select(left_hash, right_hash)?;
+            result = result.and(&previous_hash.is_eq(&equality_cmp)?)?;
             drop(ns);
 
             previous_hash =
@@ -90,7 +68,7 @@ hash_inner_node::<P::H, CRHGadget, ConstraintF>(parameters, left_hash, right_hash)?;
             i += 1;
         }
 
-        root.conditional_enforce_equal(&previous_hash, should_enforce)
+        result.and(&root.is_eq(&previous_hash)?)
     }
 }
 
@@ -235,6 +213,8 @@ - constraints_from_leaf;
             println!("constraints from path: {}", constraints_from_path);
             let leaf_g: &[_] = leaf_g.as_slice();
             cw.check_membership(&crh_parameters, &root, &leaf_g)
+                .unwrap()
+                .enforce_equal(&Boolean::TRUE)
                 .unwrap();
             if !cs.is_satisfied().unwrap() {
                 satisfied = false;

@@ -39,21 +39,11 @@ fn verify<'a, T: 'a + ToBitsGadget<ConstraintF> + ?Sized>(
         verification_key: &Self::VerificationKeyVar,
         input: impl IntoIterator<Item = &'a T>,
         proof: &Self::ProofVar,
-    ) -> Result<(), SynthesisError> {
-        Self::conditional_verify(verification_key, input, proof, &Boolean::constant(true))
-    }
-
-    fn conditional_verify<'a, T: 'a + ToBitsGadget<ConstraintF> + ?Sized>(
-        verification_key: &Self::VerificationKeyVar,
-        input: impl IntoIterator<Item = &'a T>,
-        proof: &Self::ProofVar,
-        condition: &Boolean<ConstraintF>,
-    ) -> Result<(), SynthesisError>;
+    ) -> Result<Boolean<ConstraintF>, SynthesisError>;
 
-    fn conditional_verify_prepared<'a, T: 'a + ToBitsGadget<ConstraintF> + ?Sized>(
+    fn verify_prepared<'a, T: 'a + ToBitsGadget<ConstraintF> + ?Sized>(
         prepared_verification_key: &Self::PreparedVerificationKeyVar,
         input: impl IntoIterator<Item = &'a T>,
         proof: &Self::ProofVar,
-        condition: &Boolean<ConstraintF>,
-    ) -> Result<(), SynthesisError>;
+    ) -> Result<Boolean<ConstraintF>, SynthesisError>;
 }

@@ -176,24 +176,20 @@ })
         })
     }
 
-    fn conditional_verify<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
+    fn verify<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
         vk: &Self::VerificationKeyVar,
         input: impl IntoIterator<Item = &'a T>,
         proof: &Self::ProofVar,
-        condition: &Boolean<E::Fq>,
-    ) -> Result<(), SynthesisError> {
+    ) -> Result<Boolean<E::Fq>, SynthesisError> {
         let pvk = vk.prepare()?;
-        <Self as NIZKVerifierGadget<Gm17<E, C, V>, E::Fq>>::conditional_verify_prepared(
-            &pvk, input, proof, condition,
-        )
+        <Self as NIZKVerifierGadget<Gm17<E, C, V>, E::Fq>>::verify_prepared(&pvk, input, proof)
     }
 
-    fn conditional_verify_prepared<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
+    fn verify_prepared<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
         pvk: &Self::PreparedVerificationKeyVar,
         input: impl IntoIterator<Item = &'a T>,
         proof: &Self::ProofVar,
-        condition: &Boolean<E::Fq>,
-    ) -> Result<(), SynthesisError> {
+    ) -> Result<Boolean<E::Fq>, SynthesisError> {
         let pvk = pvk.clone();
         // e(A*G^{alpha}, B*H^{beta}) = e(G^{alpha}, H^{beta}) * e(G^{psi}, H^{gamma}) *
         // e(C, H) where psi = \sum_{i=0}^l input_i pvk.query[i]
@@ -256,9 +252,7 @@ };
         let test2 = P::final_exponentiation(&test2_exp)?;
 
         let one = P::GTVar::one();
-        test1.conditional_enforce_equal(&one, condition)?;
-        test2.conditional_enforce_equal(&one, condition)?;
-        Ok(())
+        test1.is_eq(&one)?.and(&test2.is_eq(&one)?)
     }
 }
 
@@ -506,7 +500,10 @@ &vk_gadget,
                 &input_gadgets,
                 &proof_gadget,
             )
+            .unwrap()
+            .enforce_equal(&Boolean::TRUE)
             .unwrap();
+
             if !cs.is_satisfied().unwrap() {
                 println!("=========================================================");
                 println!("Unsatisfied constraints:");
@@ -648,7 +645,8 @@ <TestVerifierGadget1 as NIZKVerifierGadget<TestProofSystem1, MNT6Fq>>::verify(
                 &vk_gadget,
                 &input_gadgets,
                 &proof_gadget,
-            )?;
+            )?
+            .enforce_equal(&Boolean::TRUE)?;
             Ok(())
         }
     }
@@ -752,6 +750,8 @@ &vk_gadget,
                 &input_gadgets,
                 &proof_gadget,
             )
+            .unwrap()
+            .enforce_equal(&Boolean::TRUE)
             .unwrap();
             if !cs.is_satisfied().unwrap() {
                 println!("=========================================================");

@@ -164,24 +164,20 @@ })
         })
     }
 
-    fn conditional_verify<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
+    fn verify<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
         vk: &Self::VerificationKeyVar,
         input: impl IntoIterator<Item = &'a T>,
         proof: &Self::ProofVar,
-        condition: &Boolean<E::Fq>,
-    ) -> Result<(), SynthesisError> {
+    ) -> Result<Boolean<E::Fq>, SynthesisError> {
         let pvk = vk.prepare()?;
-        <Self as NIZKVerifierGadget<Groth16<E, C, V>, E::Fq>>::conditional_verify_prepared(
-            &pvk, input, proof, condition,
-        )
+        <Self as NIZKVerifierGadget<Groth16<E, C, V>, E::Fq>>::verify_prepared(&pvk, input, proof)
     }
 
-    fn conditional_verify_prepared<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
+    fn verify_prepared<'a, T: 'a + ToBitsGadget<E::Fq> + ?Sized>(
         pvk: &Self::PreparedVerificationKeyVar,
         public_inputs: impl IntoIterator<Item = &'a T>,
         proof: &Self::ProofVar,
-        condition: &Boolean<E::Fq>,
-    ) -> Result<(), SynthesisError> {
+    ) -> Result<Boolean<E::Fq>, SynthesisError> {
         let pvk = pvk.clone();
 
         let g_ic = {
@@ -216,10 +212,8 @@ ],
             )?
         };
 
-        let test = P::final_exponentiation(&test_exp).unwrap();
-
-        test.conditional_enforce_equal(&pvk.alpha_g1_beta_g2, condition)?;
-        Ok(())
+        let test = P::final_exponentiation(&test_exp)?;
+        test.is_eq(&pvk.alpha_g1_beta_g2)
     }
 }
 
@@ -468,6 +462,8 @@ &vk_gadget,
                 &input_gadgets,
                 &proof_gadget,
             )
+            .unwrap()
+            .enforce_equal(&Boolean::TRUE)
             .unwrap();
             if !cs.is_satisfied().unwrap() {
                 println!("=========================================================");
@@ -610,7 +606,8 @@ <TestVerifierGadget1 as NIZKVerifierGadget<TestProofSystem1, MNT6Fq>>::verify(
                 &vk_gadget,
                 &input_gadgets,
                 &proof_gadget,
-            )?;
+            )?
+            .enforce_equal(&Boolean::TRUE)?;
             Ok(())
         }
     }
@@ -714,6 +711,8 @@ &vk_gadget,
                 &input_gadgets,
                 &proof_gadget,
             )
+            .unwrap()
+            .enforce_equal(&Boolean::TRUE)
             .unwrap();
             if !cs.is_satisfied().unwrap() {
                 println!("=========================================================");

@@ -7,6 +7,7 @@
 /// Represents a variable in the constraint system which is guaranteed
 /// to be either zero or one.
 #[derive(Clone, Debug, Eq, PartialEq)]
+#[must_use]
 pub struct AllocatedBit<F: Field> {
     variable: Variable,
     cs: ConstraintSystemRef<F>,
@@ -216,6 +217,7 @@
 /// This is a boolean value which may be either a constant or
 /// an interpretation of an `AllocatedBit`.
 #[derive(Clone, Debug, Eq, PartialEq)]
+#[must_use]
 pub enum Boolean<F: Field> {
     /// Existential view of the boolean variable
     Is(AllocatedBit<F>),
@@ -245,6 +247,12 @@ }
 }
 
 impl<F: Field> Boolean<F> {
+    /// Returns the constrant `true`.
+    pub const TRUE: Self = Boolean::Constant(true);
+
+    /// Returns the constrant `false`.
+    pub const FALSE: Self = Boolean::Constant(false);
+
     pub fn lc(&self) -> LinearCombination<F> {
         match self {
             Boolean::Constant(false) => lc!(),

@@ -87,45 +87,3 @@ Ok(())
         }
     }
 }
-
-pub trait OrEqualsGadget<ConstraintF: Field>
-where
-    Self: Sized,
-{
-    /// If `should_enforce == true`, enforce that `self` equals
-    /// (a) `first` (if `cond` is `true`)
-    /// (b) `second` (if `cond` is `false`)
-    fn conditional_enforce_equal_or(
-        &self,
-        cond: &Boolean<ConstraintF>,
-        first: &Self,
-        second: &Self,
-        should_enforce: &Boolean<ConstraintF>,
-    ) -> Result<(), SynthesisError>;
-
-    fn enforce_equal_or(
-        &self,
-        cond: &Boolean<ConstraintF>,
-        first: &Self,
-        second: &Self,
-    ) -> Result<(), SynthesisError> {
-        self.conditional_enforce_equal_or(cond, first, second, &Boolean::Constant(true))
-    }
-}
-
-impl<ConstraintF, T> OrEqualsGadget<ConstraintF> for T
-where
-    ConstraintF: Field,
-    T: Sized + EqGadget<ConstraintF> + CondSelectGadget<ConstraintF>,
-{
-    fn conditional_enforce_equal_or(
-        &self,
-        cond: &Boolean<ConstraintF>,
-        first: &Self,
-        second: &Self,
-        should_enforce: &Boolean<ConstraintF>,
-    ) -> Result<(), SynthesisError> {
-        let match_opt = cond.select(first, second)?;
-        self.conditional_enforce_equal(&match_opt, should_enforce)
-    }
-}