let x be Real; :: thesis: ( 0 < x & x < 1 implies (1 + x) / (1 - x) > 0 )
assume that
A1: 0 < x and
A2: x < 1 ; :: thesis: (1 + x) / (1 - x) > 0
x ^2 < x by A1, A2, SQUARE_1:13;
then x ^2 < 1 by A2, XXREAL_0:2;
hence (1 + x) / (1 - x) > 0 by Lm4; :: thesis: verum