let r be Real; :: thesis: ( - 1 <= r & r <= 1 implies ( PI / 4 <= arccot r & arccot r <= (3 / 4) * PI ) )
assume that
A1: - 1 <= r and
A2: r <= 1 ; :: thesis: ( PI / 4 <= arccot r & arccot r <= (3 / 4) * PI )
A3: r in [.(- 1),1.] by A1, A2, XXREAL_1:1;
then r in dom (arccot | [.(- 1),1.]) by Th24, RELAT_1:62;
then (arccot | [.(- 1),1.]) . r in rng (arccot | [.(- 1),1.]) by FUNCT_1:def 3;
then arccot r in rng (arccot | [.(- 1),1.]) by A3, FUNCT_1:49;
hence ( PI / 4 <= arccot r & arccot r <= (3 / 4) * PI ) by Th56, XXREAL_1:1; :: thesis: verum