id (bool A) in Funcs ((bool A),(bool A))
by FUNCT_2:126;

then reconsider f = id (bool A) as Function of (bool A),(bool A) by FUNCT_2:66;

take f ; :: thesis: ( f is /\-preserving & f is \/-preserving )

thus ( f is /\-preserving & f is \/-preserving ) by ROUGHS_4:def 14, ROUGHS_4:def 12; :: thesis: verum

then reconsider f = id (bool A) as Function of (bool A),(bool A) by FUNCT_2:66;

take f ; :: thesis: ( f is /\-preserving & f is \/-preserving )

thus ( f is /\-preserving & f is \/-preserving ) by ROUGHS_4:def 14, ROUGHS_4:def 12; :: thesis: verum