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This is what the source actually says.
Tyril N.N. married to N.N. and later to Anna Nilsdotter Sluk, previous married to Henrik Jönsson Lapp, (they had the daughter Anna Lapp, later married to Harald Tyrilsson and mother to Anna Haraldsdotter).
Tyril's son in the first marriage, Harald Tyrilsson, married with Anna Lapp in her third marriage, first married to Henrik Persson Gyllenflög, secondly to Joen Westgöte, dead 1555 or 1556.
https://www.adelsvapen.com/genealogi/St%C3%A5lhandske_nr_98#TAB_1
Anna Nilsdotter was a sister to Tyril Nilsson Sluk, and so her line is true, the rest is false.
Anna Nilsdotter Sluk
her daughter
Anna Henriksdotter Lapp
her daughter
2. Anna Haraldsdotter, dead in the end of 1628. Married 1601-10-07 at Germundö with Erik Arvidsson Footangel, dead 1636.
Anna Haraldsdotter Stålhandske
I have no problem with Tyril being married to Anna Matsdotter Ruth, even if it doesn't have any sources, it's plausible, and you know that I'm willing to accept some level of that kind, but Tyril wasn't, and couldn't have been the son of Nils Sluk, because if he was, I'm sure that that would have prevented the marriage between Harald Tyrilsson, (his grandson) to Anna Lapp, (his granddaughter).