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The definition of 
on the base page does not read exactly as stated on the previous page. Rather, it reads:
Formally, there is no difference between the two formulations. However, the 
construct suggests to lgwam that the construct on the left hand side should be one lgwam knows from birth.
From birth, lgwam knows a finite number of constructs in addition to the four, fundamental ones mentioned in the syntax, and falsehood is one of them. We shall refer to such, extra constructs as built in constructs (in the sense of being built into lgwam). For each of the built in constructs, lgwam also knows how the construct is defined from the four, fundamental ones.
When lgwam sees an introduction, it runs through all the built in constructs it knows from birth and checks if any one of them has a definition which is identical to the right hand side of the introduction. If it finds a match, it uses the matching built in construct instead of the right hand side.
In general, computations using built in constructs are much faster than computations which use the four, fundamental constructs only.
Different implementations of lgwam may have different lists of built in constructs, but all programs will behave the same on all implementations. That is so because whenever lgwam does not recognize the right hand side of an introduction, it just uses the right hand side as it is.
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