X:
[.(PI / 4),((3 / 4) * PI ).] c= ].0 ,PI .[
by Lm9, Lm10, XXREAL_2:def 12;
A2:
[.(- 1),1.] = cot .: [.(PI / 4),((3 / 4) * PI ).]
by Th20, RELAT_1:148;
[.(- 1),1.] c= cot .: ].0 ,PI .[
by A2, X, RELAT_1:156;
hence
arccot | [.(- 1),1.] is decreasing
by Th44, RFUNCT_2:61; :: thesis: verum