let x be ext-real number ; :: thesis: ( x in REAL implies - (x + -infty ) = (- -infty ) + (- x) )
A1: - -infty = +infty by Th23;
assume A2: x in REAL ; :: thesis: - (x + -infty ) = (- -infty ) + (- x)
then x + -infty = -infty by Def2;
hence - (x + -infty ) = (- -infty ) + (- x) by A2, A1, Def2; :: thesis: verum