The autonomous vehicle is meant to drive by itself, without any driver intervention (for the levels 4 and 5 of automated driving, according to the National Highway Traffic Safety Administration(NHTSA)). This car includes a new function, called Autonomous Driving (AD) function, in charge of driving the vehicle when it is authorized. This function may be in different states (basically active or inactive), that shall be managed by a sub-function, named supervision. The main focus of this work is to ensure that the supervision of a function, performed by a safety critical embedded automotive control system (controlled systems are not considered), respects functional and safety requirements. Usually two processes are involved in the system design: the systems engineering process and the safety one. The first process defines the functional requirements on the function while the safety one specifies redundant sub-functions (realizing together the function) allowing to ensure a continuous service under failure. Since two different aspects of the system are specified, it is a major challenge to make all requirements consistent, from the outset of the design process. In this paper, a method is precisely proposed to address this issue. A progressive reinforcement of the treated requirements is achieved by means of formal state models. In fact, the proposed approach permits to build state models from requirements initially expressed in natural language. Potential ambiguities, incompletenesses or undertones in requirements are in this way gradually deleted. The enrichment of conventional formal verification of control properties with safety requirements constitutes the main originality of the deployed method and contributes to solve inconsistencies between functional and safety verification processes. In addition, the application of the method to the design of AD function supervision highlights its efficiency in an industrial context.