consider A being MSAlgebra of S such that
A1: A is gate`2=den by CIRCCOMB:def 11;
g `2 = [(g `1 ),(the Charact of A . g)] `2 by A1, CIRCCOMB:def 10
.= the Charact of A . g by MCART_1:7
.= Den g,A by MSUALG_1:def 11 ;
hence ( g `2 is Function-like & g `2 is Relation-like ) ; :: thesis: verum