Theory Washing

(*  Title:      Sequents/Washing.thy
    Author:     Sara Kalvala
*)

theory Washing
imports ILL
begin

consts
  dollar :: o
  quarter :: o
  loaded :: o
  dirty :: o
  wet :: o
  clean :: o

axioms
  change:
  "dollar |- (quarter >< quarter >< quarter >< quarter)"

  load1:
  "quarter , quarter , quarter , quarter , quarter |- loaded"

  load2:
  "dollar , quarter |- loaded"

  wash:
  "loaded , dirty |- wet"

  dry:
  "wet, quarter , quarter , quarter |- clean"


(* "activate" definitions for use in proof *)

ML {* bind_thms ("changeI", [@{thm context1}] RL ([@{thm change}] RLN (2,[@{thm cut}]))) *}
ML {* bind_thms ("load1I", [@{thm context1}] RL ([@{thm load1}] RLN (2,[@{thm cut}]))) *}
ML {* bind_thms ("washI", [@{thm context1}] RL ([@{thm wash}] RLN (2,[@{thm cut}]))) *}
ML {* bind_thms ("dryI", [@{thm context1}] RL ([@{thm dry}] RLN (2,[@{thm cut}]))) *}

(* a load of dirty clothes and two dollars gives you clean clothes *)

lemma "dollar , dollar , dirty |- clean"
  apply (tactic {* best_tac (lazy_cs add_safes (@{thms changeI} @ @{thms load1I} @ @{thms washI} @ @{thms dryI})) 1 *})
  done

(* order of premises doesn't matter *)

lemma "dollar , dirty , dollar |- clean"
  apply (tactic {* best_tac (lazy_cs add_safes (@{thms changeI} @ @{thms load1I} @ @{thms washI} @ @{thms dryI})) 1 *})
  done

(* alternative formulation *)

lemma "dollar , dollar |- dirty -o clean"
  apply (tactic {* best_tac (lazy_cs add_safes (@{thms changeI} @ @{thms load1I} @ @{thms washI} @ @{thms dryI})) 1 *})
  done

end