let X be non empty TopSpace; :: thesis: for A, B being Subset of X
for U being a_neighborhood of B st A c= B holds
U is a_neighborhood of A
let A, B be Subset of X; :: thesis: for U being a_neighborhood of B st A c= B holds
U is a_neighborhood of A
let U be a_neighborhood of B; :: thesis: ( A c= B implies U is a_neighborhood of A )
assume A1: A c= B ; :: thesis: U is a_neighborhood of A
B c= Int U by CONNSP_2:def 2;
hence A c= Int U by A1; :: according to CONNSP_2:def 2 :: thesis: verum