theorem
  F is commutative associative & c1 <> c2 & c1 <> c3 & c2 <> c3 implies
  F $$ ({.c1,c2,c3.},f) = F.(F.(f.c1, f.c2),f.c3)
proof
  assume that
A1: F is commutative associative and
A2: c1 <> c2;
  assume c1 <> c3 & c2 <> c3;
  then
A3: not c3 in {c1,c2} by TARSKI:def 2;
  thus F $$ ({.c1,c2,c3.},f) = F $$ ({.c1,c2.} \/ {.c3.},f) by ENUMSET1:3
    .= F.(F $$ ({.c1,c2.},f),f.c3) by A1,A3,Th2
    .= F.(F.(f.c1, f.c2),f.c3) by A1,A2,Th1;
end;
