That sounds a bit like Hoare logic [0], refinement calculus [1], or guarded command language [2]. The term "program prime" is not something I've heard or read before and I'm not turning up much.
Goodness knows why my original comment is being downvoted. The formal term is 'primary program refinement' and can be found all over the place such as here:
[0] https://en.wikipedia.org/wiki/Hoare_logic
[1] https://en.wikipedia.org/wiki/Refinement_calculus
[2] https://en.wikipedia.org/wiki/Guarded_Command_Language