Definition
The h-principle
Every formal solution can be deformed through formal solutions to an actual jet solution.
A differential relation satisfies the h-principle in the nonparametric sense if every formal solution is joined by a homotopy through formal solutions to a holonomic solution. The regularity of sections and homotopies is part of the convention.
Variants
Relative, parametric, and approximation forms impose additional requirements. They are stronger statements and must be specified when used.