<steps up to the begats plate
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Yes, Edward I "Longshanks" was Edward IIIs grandfather. Edward IIIs father & Edward Is son being the unfortunate & deposed Edward II.
Now as for the Six Wives all being descended from them....
Catherine of Aragon - comes from John of Gaunt, EIIIs son....after his marriage to Constance of Castile in his futile bid to gain a crown for himself, his daughter Philippa (from his first marriage to Blanche of Lancaster) was married to John I of Portugal; their granddaughter Isabel married into Spain (as the Iberians were wont to do). Off the top of my head it fails me as to whether she was the ancestress of Ferdinand or Isabella....I'm pretty sure it was Isabella....Catherine's parents.
Anne Boleyn - is actually from EIs second marriage to Marguerite of France AND his first marriage to Eleanor of Castile. Edward & Eleanor's daughter Margaret married John of Brabant; their son John married another Margaret, this one the daughter of Edward & Marguerite's son, Thomas of Brotherton. Margaret's daughter Elizabeth (by her second marriage, not the Brabant one)married into the Mowbrays, who married into the Howards (which is where the Howards claimed the dukedom of Norfolk as there were no more Mowbray male heirs), who married into the Boleyns.
Jane Seymour - comes from Lionel of Antwerp, EIIIs son. Lionel's only child Philippa married into the Mortimers....Philippa's daughter Elizabeth married Henry "Hotspur" Percy....her great-great granddaughter Margaret married Sir John Seymour...they were Jane's parents.
Anne of Cleves - comes thru the aforementioned Brabant alliance....the daughter of that marriage, another Margaret, married a count of Flanders....her daughter, another Margaret, married Philip "the Bold" of Burgundy....& their granddaughter Mary wed a duke of Cleves....Anne's great-great-grandfather.
Catherine Howard - same as Anne Boleyn natch
Catherine Parr - comes thru John of Gaunt on the distaff side. Joan Beaufort, Gaunt's daughter by his third wife Catherine Swynford (but whose birth preceded the marriage as Gaunt was chasing after Castilian crowns & apparently that was a bit more important), married into the Nevilles (the Kingmaker was her grandson)....her granddaughter Alice Neville's daughter Elizabeth Fitzhugh married Sir William Parr....Catherine's grandfather.
I think I got the important bits ROFL