More on Le and Lt

This module gives some additionnal lemmas to the modules Le and Lt of the distribution; in the statements and proofs, we use the constants one, ..., four declared in the module Constants .

Click here to look at the source .

For the beginner ...

The lemma
le5:(P:nat->Prop)
        (P O)->
        (P one)->
        (P two)->
        (P three)->
        (P four) ->
        ((n:nat)(lt four n)->(P n))->
        (n:nat)(P n).
is used as a first step in the proof of:
Lemma enum4:(n:nat)(lt n (S four))->
            n=O\/n=one\/n=two\/n=three\/n=four.
Which is done by a classical Pattern ...; Apply sequence.

enum4 is used in generation to prove that every n >5 is either 3, either a power of 2.