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% demonstrate an induction performed automatically.
% prove the associative law of addition by induction from the definition.


set(lambda).
set(binary_res).
set(induction).
set(demod_inf).
set(para_into).
set(para_from).
weight_list(pick_and_purge).
weight(g($(0)),1).   %every g-term counts like a constant
end_of_list.


list(demodulators).
x+0 = x.
x*0 = 0.
end_of_list.

list(usable).
x = x.         
s(x) != s(y) | x = y.
s(x) != 0.
-ap(y,0) | ap(y,g(y)) | ap(y,z).
-ap(y,0) | -ap(y,s(g(y))) | ap(y,z).
x + s(y) = s(x + y).
x * s(y) = x * y + x.
end_of_list.

list(sos).
(a + b) + n != a + (b + n).
end_of_list.