deffunc H₄( Subset of X, Subset of X) -> Element of bool X = $1 \/ $2;
consider j being BinOp of (bool X) such that
A1: for x, y being Subset of X holds j . (x,y) = H₄(x,y) from BINOP_1:sch 4();
deffunc H₅( Subset of X, Subset of X) -> Element of bool X = $1 /\ $2;
consider m being BinOp of (bool X) such that
A2: for x, y being Subset of X holds m . (x,y) = H₅(x,y) from BINOP_1:sch 4();
take LattStr(# (bool X),j,m #) ; :: thesis: ( the carrier of LattStr(# (bool X),j,m #) = bool X & ( for Y, Z being Subset of X holds
( the L_join of LattStr(# (bool X),j,m #) . (Y,Z) = Y \/ Z & the L_meet of LattStr(# (bool X),j,m #) . (Y,Z) = Y /\ Z ) ) )
thus ( the carrier of LattStr(# (bool X),j,m #) = bool X & ( for Y, Z being Subset of X holds
( the L_join of LattStr(# (bool X),j,m #) . (Y,Z) = Y \/ Z & the L_meet of LattStr(# (bool X),j,m #) . (Y,Z) = Y /\ Z ) ) ) by A1, A2; :: thesis: verum