A "Scholastic" approach to theology might progress from apparently given fixed principles through apparently syllogistic logic to apparently obvious conclusions. Thus:-
"Popes do not Teach heresy;
Honorius taught heresy;
Therefore Honorius was not pope"
"Antipopes have no legitimate jurisdiction;
Honorius was an antipope;
Therefore Honorius had no jurisdiction."
and so on; thus the canonical framework Honorius imposed upon the Anglo-Saxon Church was of no effect. Et cetera; et cetera.
You could put a group of such thinkers on to a Desert Island, and by pure logic they could come up with a complete history of the Church, perfect in every respect, possibly even armoured by every protection of immaculate logic ... except that it bore no relationship to what actually did happen in the real History of the real Church.
Thus, although Pope Honorius was condemned by his successors and anathematised by an Ecumenical Council, nobody ever did claim that he at any point ceased to be pope; or that his acts of papal jurisdiction were "invalid", in England or anywhere else. Certainly, when S Bede the Venerable wrote his account of the Honorius years, there is no hint in the Saint's words that Honorius was an antipope or that his acts of jurisdiction were null. Nor did later popes or Ecumenical Councils decree this to be so.
More later ... perhaps after, tomorrow, I have lauded that faultless pontiff Prospero Lambertini..