(* 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