Mary Cantrill bp 3 Jan 1664 at Ashover, parents William Cantrill and Elizabeth Ward, who married 16 Jun 1663 at Ashover. The transcriptions from Derbyshire actually give this as "Mary Simwill" of Doe Hole Lane, Ashover, but looking at the original, the surname is clearly wrong, and could be Carnwill, Cainvill or Cantrill. Married Joseph Oates 4 Jun 1681 in Dronfield (Dronfield 12 m N Ashover). In the wedding certificate it indicates that they were from "Dore", a village about 4 miles NW of Dronfield. If Mary was from Ashover, this could mean that Joseph was from Dore, or, alternatively, that they were living in Dore when they married. Apart from the birth in Ashover, there are no other births for either Mary Carnall or Joseph Oates in the area around Dronfield.
Alternative family for Mary: Mary Carnall could have been the daughter of John Carnall, who married Anna Stephenson 22 Sep 1653 at Hathersage, Derbyshire. Hathersage is 6 miles west of Dore. The evidence is slight if non-existent, and is based mainly on the fact that in the wedding certificate of John and Anna it states "Johannes Carnall et Ann Stephenson de Dore", thus indicating that one or both was from Dore. Other circumstantial evidence includes:
there is a child Anne Carnell bp 18 Nov 1655 at Great Longstone (8m south Hathersage), father according to ancestry Thomas but if you look at the original it could well be Johannes.
there is the baptism of Sarah Carnill at Dronfield 7 Jun 1660, father John.
Thomas Carnill baptised 26 Mar 1670 at Dronfield, father John. This would indicate that the John Carnill family was still living in Dronfield in 1670. Unfortunately there doesn't seem to be a daughter Mary either in Hathersage 1653-1660 or in Dronfield 1660-1663. This cut-off date of 1663 is because "our" Mary married in 1681, so then she would have been 18 years old if born in 1663.