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subsection {* Ports *}
theory Ports
imports Main
begin

text{*
  This theory can be used if we want to specify the port numbers by names denoting their default 
  Integer values. If you want to use them, please add @{text Ports} to the simplifier.
*}

definition http::int where "http = 80"

lemma http1: "x \<noteq> 80 \<Longrightarrow> x \<noteq> http"
by (simp add: http_def)

lemma http2: "x \<noteq> 80 \<Longrightarrow> http \<noteq> x"
by (simp add: http_def)


definition smtp::int where "smtp = 25"

lemma smtp1: "x \<noteq> 25 \<Longrightarrow> x \<noteq> smtp"
by (simp add: smtp_def)

lemma smtp2: "x \<noteq> 25 \<Longrightarrow> smtp \<noteq> x"
by (simp add: smtp_def)


definition ftp::int where "ftp = 21"

lemma ftp1: "x \<noteq> 21 \<Longrightarrow> x \<noteq> ftp"
by (simp add: ftp_def)

lemma ftp2: "x \<noteq> 21 \<Longrightarrow> ftp \<noteq> x"
by (simp add: ftp_def)

text{* And so on for all desired port numbers. *}

lemmas Ports = http1 http2 ftp1 ftp2 smtp1 smtp2

end