Sindbad~EG File Manager

% composition of group homomorphisms is a homomorphism

set(lambda).
set(demod_inf).
set(para_into).
set(para_from).
assign(max_distinct_vars,0).

% Hom(xG,xH,xPhi) means Phi is a homomorphism from G to H
% that is,  forall x,y in xG, we have  Phi(x*y) = Phi(x) * Phi(y) and  Phi(i(x)) = i(Phi(y)).

list(usable).
Ap(G,x) != $T  |  Ap(H,Ap(Phi,x)) = $T.      % Phi maps G to H
Ap(H,x) != $T  |  Ap(K,Ap(Psi,x)) = $T.      % Psi maps H to K
Ap(G,x) != $T | Ap(G,y) != $T |  Ap(Phi,x*y) = Ap(Phi,x) * Ap(Phi,y).   %Phi preserves product on G
Ap(G,x) != $T | Ap(Phi,i(x)) = i(Ap(Phi,x)).                            %Phi preserves inverse
Ap(H,x) != $T | Ap(H,y) != $T |  Ap(Psi,x*y) = Ap(Psi,x) * Ap(Psi,y).   %Psi preserves product on H
Ap(H,x) != $T | Ap(Psi,i(x)) = i(Ap(Psi,x)).                            %Psi preserves inverse
Ap(G,a) = $T.
Ap(G,b) = $T.
end_of_list.

list(demodulators).
Ap(G,a) = $T.
Ap(G,b) = $T.
Chi = lambda(x,Ap(Psi,Ap(Phi,x))).            % Chi is the composition of Phi and Psi
(x=x) = $T.
end_of_list.

list(sos).
Ap(Chi,a*b) != Ap(Chi,a) * Ap(Chi,b)  | Ap(Chi,i(a)) != i(Ap(Chi,a)) |  Ap(K,Ap(Chi,a)) != $T.
end_of_list.