private static bool UpdateColumnNamesForTableSharing(
            DbDatabaseMapping databaseMapping, EdmEntityType entityType, DbTableMetadata toTable,
            DbEntityTypeMappingFragment fragment)
        {
            // Validate: this table can be used only if:
            //  1. The table is not used by any other type
            //  2. The table is used only by types in the same type hierarchy (TPH)
            //  3. There is a 1:1 relationship and the PK count and types match (Table Splitting)
            var typesSharingTable = FindAllTypesUsingTable(databaseMapping, toTable);
            var associationsToSharedTable = new Dictionary<EdmEntityType, List<EdmAssociationType>>();

            foreach (var candidateType in typesSharingTable)
            {
                var oneToOneAssocations = FindAllOneToOneFKAssociationTypes(
                    databaseMapping.Model, entityType, candidateType);

                var rootType = candidateType.GetRootType();
                if (!associationsToSharedTable.ContainsKey(rootType))
                {
                    associationsToSharedTable.Add(rootType, oneToOneAssocations.ToList());
                }
                else
                {
                    associationsToSharedTable[rootType].AddRange(oneToOneAssocations);
                }
            }
            foreach (var candidateTypePair in associationsToSharedTable)
            {
                // Check if these types are in a TPH hierarchy
                if (candidateTypePair.Key != entityType.GetRootType()
                    &&
                    candidateTypePair.Value.Count == 0)
                {
                    var tableName = toTable.GetTableName();
                    throw Error.EntityMappingConfiguration_InvalidTableSharing(
                        entityType.Name, candidateTypePair.Key.Name,
                        tableName != null ? tableName.Name : toTable.DatabaseIdentifier);
                }
            }

            var allAssociations = associationsToSharedTable.Values.SelectMany(l => l);
            if (allAssociations.Any())
            {
                var principalKeyNamesType = toTable.GetKeyNamesType();
                if (principalKeyNamesType == null)
                {
                    // grab a candidate
                    var association = allAssociations.First();
                    principalKeyNamesType = association.Constraint.PrincipalEnd(association).EntityType;

                    if (allAssociations.All(x => x.Constraint.PrincipalEnd(x).EntityType == principalKeyNamesType))
                    {
                        toTable.SetKeyNamesType(principalKeyNamesType);
                    }
                }

                // rename the columns in the fragment to match the principal keys
                var principalKeys = principalKeyNamesType.KeyProperties().ToArray();
                var i = 0;
                foreach (var k in entityType.KeyProperties())
                {
                    var dependentColumn = fragment.PropertyMappings.Single(pm => pm.PropertyPath.First() == k).Column;
                    dependentColumn.Name = principalKeys[i].Name;
                    i++;
                }
                return true;
            }
            return false;
        }