0 a form of a word that appears as an entry in a dictionary and is used to represent all the other possible forms. For example, the lemma "build" represents "builds", "building", "built", etc.: --
We conclude by coinduction that the conclusion of the lemma holds for all typed assertions.
As r and d involve only single instantiations, not general substitution, the proofs of those results do not need the usual substitution lemma.
Since assignments are total functions, the following substitution lemma is true only under condition that s is defined.
Lemma 4.4 plays a key role in this proof.
If it does not touch a hole, then i+1 is given by the uniform transition lemma.
First, we need a lemma that shows that the translated term simulates the behavior of the original term in some way.
Following the construction of the previous section, we obtain the following lemma.
In the next section, we shall need the following technical lemma.
