Abstract : For the study of the proof we adapt Toulmin's theoretical frame on arguments of plausibility and arguments of necessity to Chevallard's anthropological theory of didactics. The validations of mathematic teaching are the double transposition of proofs from the mathematical institution (producing the knowledge) and validations (argumentations and proofs) from other institutions (like the “daily life”). The diachronic study of curricula of French ‘collège-lycée' and of German Gymnasium (in Baden-Württemberg), confirmed by the study of textbooks shows that proof is explicitly taught as opposed to the cases of Realschule and Hauptschule. These curricula advise the use of different types of validation (argumentation, proof) and arguments (pragmatic, semantic, syntactic) depending on the functions and when they are introduced. The influence of the functions of validation on the different types of tasks (discovering, controlling, changing registers, ...) are also observed in lessons on proof. In spite of linguistic, institutional, and cultural difficulties in comparing France and Germany, the study of validations, of class theorems in textbooks, and of proofs produced by students, shows similarities about combining different types of arguments as well as different types of functions. Differences are observed on the types of technology and technique involved in the validation and on the weight given to different types of arguments and registers used, with an explanation related to the institutional conditions (moment of introduction, didactical contract, function, educational system, ...).