diff --git a/Kernel_d/doc/Kernel_d/Concepts/LinearAlgebraTraits_d.h b/Kernel_d/doc/Kernel_d/Concepts/LinearAlgebraTraits_d.h
index 27551d725a1..932880c6f89 100644
--- a/Kernel_d/doc/Kernel_d/Concepts/LinearAlgebraTraits_d.h
+++ b/Kernel_d/doc/Kernel_d/Concepts/LinearAlgebraTraits_d.h
@@ -118,7 +118,7 @@ and the columns of `spanning_vectors` are a maximal set of
 linearly independent solutions to the corresponding homogeneous
 system.
 
-\pre `M.row_dimension() = b.dimension()`.
+\pre `M.row_dimension() == b.dimension()`.
 */
 static bool linear_solver(const Matrix& M, const Vector& b,
 Vector& x, NT& D, Matrix& spanning_vectors, Vector& c);
@@ -127,14 +127,14 @@ Vector& x, NT& D, Matrix& spanning_vectors, Vector& c);
 determines whether the linear
 system \f$ M\cdot x = b\f$ is solvable. If yes, then \f$ (1/D) x\f$ is a
 solution, if not then \f$ c^T \cdot M = 0\f$ and \f$ c^T \cdot b \not= 0\f$.
-\pre `M.row_dimension() = b.dimension()`.
+\pre `M.row_dimension() == b.dimension()`.
 */
 static bool linear_solver(const Matrix& M, const Vector& b,
 Vector& x, NT& D, Vector& c) ;
 
 /*!
 as above, but without the witness \f$ c\f$
-\pre `M.row_dimension() = b.dimension()`.
+\pre `M.row_dimension() == b.dimension()`.
 */
 static bool linear_solver(const Matrix& M, const Vector& b,
 Vector& x, NT& D) ;
@@ -142,7 +142,7 @@ Vector& x, NT& D) ;
 /*!
 determines whether the system \f$ M \cdot x = b\f$ is solvable
 
-\pre `M.row_dimension() = b.dimension()`.
+\pre `M.row_dimension() == b.dimension()`.
 */
 static bool is_solvable(const Matrix& M, const Vector& b)
 ;
diff --git a/Kernel_d/doc/Kernel_d/Concepts/Matrix.h b/Kernel_d/doc/Kernel_d/Concepts/Matrix.h
index 7a2c7d96e1a..f2daec7a033 100644
--- a/Kernel_d/doc/Kernel_d/Concepts/Matrix.h
+++ b/Kernel_d/doc/Kernel_d/Concepts/Matrix.h
@@ -325,7 +325,7 @@ Matrix operator-();
 /*!
 Multiplication.
 
-\pre `M.column_dimension() = M1.row_dimension()`
+\pre `M.column_dimension() == M1.row_dimension()`
 */
 Matrix operator*(const Matrix& M1)
 ;
@@ -334,7 +334,7 @@ Matrix operator*(const Matrix& M1)
 Multiplication with
 vector.
 
-\pre `M.column_dimension() = vec.dimension()`
+\pre `M.column_dimension() == vec.dimension()`
 */
 Vector operator*(const Vector& vec) ;
 
diff --git a/Kernel_d/doc/Kernel_d/Concepts/Vector.h b/Kernel_d/doc/Kernel_d/Concepts/Vector.h
index d5bfe190fa0..99214f381a3 100644
--- a/Kernel_d/doc/Kernel_d/Concepts/Vector.h
+++ b/Kernel_d/doc/Kernel_d/Concepts/Vector.h
@@ -119,14 +119,14 @@ Vector operator+(const Vector& v1) ;
 /*!
 Subtraction.
 
-\pre `v.dimension() = v1.dimension()`.
+\pre `v.dimension() == v1.dimension()`.
 */
 Vector operator-(const Vector& v1) ;
 
 /*!
 Inner Product.
 
-\pre `v.dimension() = v1.dimension()`.
+\pre `v.dimension() == v1.dimension()`.
 */
 NT operator*(const Vector& v1) ;