let R be RelStr ; :: thesis: for S being Subset of R
for C being Clique of (subrelstr S) holds C is Clique of R
let S be Subset of R; :: thesis: for C being Clique of (subrelstr S) holds C is Clique of R
let C be Clique of (subrelstr S); :: thesis: C is Clique of R
Aa: the carrier of (subrelstr S) = S by YELLOW_0:def 15;

now

let a, b be Element of R; :: thesis: ( a in C & b in C & a <> b & not a <= b implies b <= a )
assume that
A1: a in C and
B1: b in C and
C1: a <> b ; :: thesis: ( a <= b or b <= a )
reconsider a9 = a, b9 = b as Element of (subrelstr S) by A1, B1;
( a9 <= b9 or b9 <= a9 ) by A1, B1, C1, DClique;
hence ( a <= b or b <= a ) by YELLOW_0:60; :: thesis: verum

end;

hence C is Clique of R by Aa, XBOOLE_1:1, DClique; :: thesis: verum