Hi,

I am reading this book and there is an attempt to prove a concept by describin it and it is pretty vague what technique the writter is using to prove it. I mannaged to break his "proof" into variables and statements. so i have 4 variables

$\displaystyle y_{c}, x_{c}, k, c$

and the statemant the author is trying to prove is

$\displaystyle \forall x_{c} \in Z_{+}, y_{c} \geq x_{c}-k+1$

the tricky part is that it appears the following statements hold

$\displaystyle c>0, y_{c} =c$

$\displaystyle c=1, x_{c} = c+k+1$

and

$\displaystyle c>1, x_{c-1} +k +1\geq x_{c}\geq x_{c-1}$

but are not given in his formulation of what i call " his lemma".

so since i am new to discrete math, then if there is no clear formulation of the problem i don't know what strategy should i choose to prove the statement, i need some help.

my question is : To prove the statement, should i break it into cases? or is this a clasical case where one shoul use induction and treat c=1 as base case ? but what is the induction hypothesis then?. And how, one should formulate the statement correctly if one know the above stated facts.

As you can see I am confused. I would love to post the original text but it is in Macedonian and it is about the beauty of the mountain. so i doubt that anyone would invest his/hers time to break it into pieces and mess with it.

thank you in advance

baxy