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Interlude 1: Some lemmas needed for intersections

After initial troubles proving the basic properties of kintersection defined in the next major section, I thought a series of simple lemmas might help. One of them was never used in later proofs.
list(usable).
a(charq,eq) = p1.
end_of_list.

Proof of a(charq,eq) = p1. | OTTER output file


list(usable).
a(charq,xf) = p2 | a(a(xf,x),pair(p1,p2)) = a(xf,x).     %    (not used in later proofs)
end_of_list.

Proof of a(charq,xf) = p2 | a(a(xf,x),pair(p1,p2)) = a(xf,x). | OTTER output file


list(usable).
a(a(abst,k(x)),k(y)) = k(a(x,y)).
end_of_list.

list(demodulators).
a(a(abst,k(x)),k(y)) = k(a(x,y)).
end_of_list.

Proof of a(a(abst,k(x)),k(y)) = k(a(x,y)). | OTTER output file


list(usable).
pair(x1,y1) != pair(x2,y2) | x1 = x2.
end_of_list.

Proof of pair(x1,y1) != pair(x2,y2) | x1 = x2. | OTTER output file


list(usable).
pair(x1,y1) != pair(x2,y2) | y1 = y2.
end_of_list.

Proof of pair(x1,y1) != pair(x2,y2) | y1 = y2. | OTTER output file


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