let a, b, c, d be Real; :: thesis: ( a < b & c < d implies Fr (closed_inside_of_rectangle (a,b,c,d)) = rectangle (a,b,c,d) )
assume that
A1: a < b and
A2: c < d ; :: thesis: Fr (closed_inside_of_rectangle (a,b,c,d)) = rectangle (a,b,c,d)
set P = closed_inside_of_rectangle (a,b,c,d);
thus Fr (closed_inside_of_rectangle (a,b,c,d)) = (closed_inside_of_rectangle (a,b,c,d)) \ (Int (closed_inside_of_rectangle (a,b,c,d))) by TOPS_1:43
.= (closed_inside_of_rectangle (a,b,c,d)) \ (inside_of_rectangle (a,b,c,d)) by A1, A2, Th50
.= rectangle (a,b,c,d) by A1, A2, Th51 ; :: thesis: verum