demonstrate vs prove out

demonstrate

verb
  • to show, display, or present; to prove or make evident 

  • to show the steps taken to create a logical argument or equation. 

  • to show how to use (something). 

  • to participate in or organize a demonstration. 

prove out

verb
  • To demonstrate the feasibility of; to show or be shown to be feasible, accurate, true, satisfactory, as expected, hoped, stated, etc. 

  • To turn out to be feasible, accurate, true, satisfactory, as expected, hoped, stated, etc. 

How often have the words demonstrate and prove out occurred in a corpus of books? (source: Google Ngram Viewer )