let X be set ; :: thesis: for L being List of X
for O being Operation of X st L c= dom O holds
L WHERE O = L
let L be List of X; :: thesis: for O being Operation of X st L c= dom O holds
L WHERE O = L
let O be Operation of X; :: thesis: ( L c= dom O implies L WHERE O = L )
assume A1: L c= dom O ; :: thesis: L WHERE O = L
thus L WHERE O c= L by Th4; :: according to XBOOLE_0:def 10 :: thesis: L c= L WHERE O
let z be object ; :: according to TARSKI:def 3 :: thesis: ( not z in L or z in L WHERE O )
assume A2: z in L ; :: thesis: z in L WHERE O
then reconsider z = z as Element of X ;
z . O <> {} by A1, A2, RELAT_1:170;
hence z in L WHERE O by A2, Th3; :: thesis: verum