An internal model of mathematical practice for interactive systems of theorem proof construction. Part 1. General model description

A model of mathematical practice is offered for developing interactive systems of correct proofs construction for mathematical statements on the basis of mathematical knowledge. This model is more adequate than mathematical logic models. The model of the mathematical practice is represented as a combination of two models. The first one is an internal model, i.e., a formal system. The second one is an external model. In the framework of the external model, a mathematician can control the process of intuitive proofs construction. Requirements to the external and internal models of the mathematical practice are formulated. A generic description of the internal model is included.