let X be non empty TopSpace; :: thesis: for Y0 being non empty open SubSpace of X
for A being Subset of X
for B being Subset of Y0 st A = B holds
Int A = Int B
let Y0 be non empty open SubSpace of X; :: thesis: for A being Subset of X
for B being Subset of Y0 st A = B holds
Int A = Int B
reconsider C = the carrier of Y0 as Subset of X by TSEP_1:1;
let A be Subset of X; :: thesis: for B being Subset of Y0 st A = B holds
Int A = Int B
let B be Subset of Y0; :: thesis: ( A = B implies Int A = Int B )
A1: C is open by TSEP_1:16;
assume A = B ; :: thesis: Int A = Int B
hence Int A = Int B by A1, Th57; :: thesis: verum