let A be non empty Subset of ExtREAL; :: thesis: ( ( for r being Element of ExtREAL st r in A holds

r <= -infty ) implies A = {-infty} )

assume A1: for r being Element of ExtREAL st r in A holds

r <= -infty ; :: thesis: A = {-infty}

assume A <> {-infty} ; :: thesis: contradiction

then ex a being Element of A st a <> -infty by SETFAM_1:49;

hence contradiction by A1, XXREAL_0:6; :: thesis: verum

r <= -infty ) implies A = {-infty} )

assume A1: for r being Element of ExtREAL st r in A holds

r <= -infty ; :: thesis: A = {-infty}

assume A <> {-infty} ; :: thesis: contradiction

then ex a being Element of A st a <> -infty by SETFAM_1:49;

hence contradiction by A1, XXREAL_0:6; :: thesis: verum