happen vs prove out

happen

verb
  • To occur or take place. 

  • To do or occur by chance or unexpectedly. 

  • To encounter by chance. 

prove out

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

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

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