let a, b, c be ext-real number ; :: thesis: ( a in REAL & a <= b & b < c implies b in REAL )
assume that
A1: a in REAL and
A2: a <= b and
A3: b < c ; :: thesis: b in REAL
( b in REAL or b = +infty ) by A1, A2, Th10;
hence b in REAL by A3, Lm8; :: thesis: verum