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The lemma and form together make up the information associated with the lexical entry for each word in the lexicon.
The lemmatised form is simply a convenient representation of the headword lemma.
During the lemma selection process, semantically and syntactically appropriate lexical items are selected from the mental lexicon.
The first part of the lemma below also follows by construction.
The lemma below states that any two types, that are convertible after an application of small substitutions, have equal interpretations.
We start with a preliminary lemma, which states that proper has indeed the desired effect.
T he next lemma shows how context-sensitive reduction steps are simulated by the second transformation.
The following lemma follows immediately from (2.2) and properties of the norm residue symbol.
This leads to a contradiction and ends the first part of the lemma.
To define the section at these places we shall need the following simple lemma.
In the next section, we shall need the following technical lemma.
Following the construction of the previous section, we obtain the following lemma.
First, we need a lemma that shows that the translated term simulates the behavior of the original term in some way.
If it does not touch a hole, then i+1 is given by the uniform transition lemma.
Lemma 4.4 plays a key role in this proof.
Since assignments are total functions, the following substitution lemma is true only under condition that s is defined.
As r and d involve only single instantiations, not general substitution, the proofs of those results do not need the usual substitution lemma.
We conclude by coinduction that the conclusion of the lemma holds for all typed assertions.
