Both Uses

establish
in
The Crucible
(Edited)

Salem had been established hardly forty years before.
p. 4.3 *

established = founded (started)
DANFORTH—(his first real outburst, in which his contempt for Parris is clear): Mr. Parris, I bid you be silent! (He stands in silence, looking out the window. Now, having established that he will set the gait.) Mr. Cheever, will you go into the court and bring the children here?
p. 101.3 *

established = demonstrated

editor's notes: By "he will set the gait," Miller is saying that Danforth will be in charge--like someone who controls the gait/pace at which a horse moves.

Definitions:

(1) (establish as in: establish a positive tone)
create, start, or set in [a] place
(2) (establish as in: establish that there is a need)
show or determine (cause to be recognized or figure out)
(3) (meaning too rare to warrant focus)