set f = sec | ].(PI / 2),PI .];
A1:
(sec | ].(PI / 2),PI .]) | ].(PI / 2),PI .] = sec | ].(PI / 2),PI .]
by RELAT_1:102;
A2:
(sec | ].(PI / 2),PI .]) | ].(PI / 2),PI .] is increasing
by Th18;
(sec | ].(PI / 2),PI .]) .: ].(PI / 2),PI .] =
rng ((sec | ].(PI / 2),PI .]) | ].(PI / 2),PI .])
by RELAT_1:148
.=
rng (sec | ].(PI / 2),PI .])
by RELAT_1:102
.=
sec .: ].(PI / 2),PI .]
by RELAT_1:148
;
hence
arcsec2 | (sec .: ].(PI / 2),PI .]) is increasing
by A1, A2, FCONT_3:17; :: thesis: verum