Cole Stole?

I was watching Lady Of The Tropics (1939), starring Hedy Lamarr (the main reason I was watching), and early on there was a scene set in a nightclub.  The singer started a number with a lyric I thought very familiar. I didn't recognize the tune, but the words sure sounded like "Every time we say goodbye/ I die a little." Wow.

I checked, and I was a bit off.  The song, according to the IMDb, is "Each Time You Say Goodbye (I Die A Little)."  It's by Phil Ohman and Foster Carling and sung by Gloria Franklin who was actually dubbed by Harriet Cruise.  Still...

The song "Ev'ry Time We Say Goodbye," starting with the same words (except for "Each"), is a Cole Porter tune that's become part of the Great American Songbook.  It was introduced in a 1944 Billy Rose extravaganza known as Seven Lively Arts.  The show was not a hit, but the song has lived on.

Since it was first performed five years after Lady Of The Tropics, it makes you wonder if Cole Porter stole the words, even if he didn't think much of the tune.  Maybe it was just something he had in the back of his mind.  In any case, it's so close I have to believe it's more than a coincidence.