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(* Title: Sequents/Washing.thy
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Author: Sara Kalvala
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*)
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theory Washing
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imports ILL
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begin
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consts
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dollar :: o
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quarter :: o
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loaded :: o
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dirty :: o
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wet :: o
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clean :: o
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axioms
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change:
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"dollar |- (quarter >< quarter >< quarter >< quarter)"
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load1:
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"quarter , quarter , quarter , quarter , quarter |- loaded"
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load2:
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"dollar , quarter |- loaded"
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wash:
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"loaded , dirty |- wet"
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dry:
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"wet, quarter , quarter , quarter |- clean"
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(* "activate" definitions for use in proof *)
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ML {* bind_thms ("changeI", [@{thm context1}] RL ([@{thm change}] RLN (2,[@{thm cut}]))) *}
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ML {* bind_thms ("load1I", [@{thm context1}] RL ([@{thm load1}] RLN (2,[@{thm cut}]))) *}
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ML {* bind_thms ("washI", [@{thm context1}] RL ([@{thm wash}] RLN (2,[@{thm cut}]))) *}
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ML {* bind_thms ("dryI", [@{thm context1}] RL ([@{thm dry}] RLN (2,[@{thm cut}]))) *}
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(* a load of dirty clothes and two dollars gives you clean clothes *)
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lemma "dollar , dollar , dirty |- clean"
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apply (tactic {* best_tac (lazy_cs add_safes (@{thms changeI} @ @{thms load1I} @ @{thms washI} @ @{thms dryI})) 1 *})
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done
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(* order of premises doesn't matter *)
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lemma "dollar , dirty , dollar |- clean"
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apply (tactic {* best_tac (lazy_cs add_safes (@{thms changeI} @ @{thms load1I} @ @{thms washI} @ @{thms dryI})) 1 *})
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done
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(* alternative formulation *)
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lemma "dollar , dollar |- dirty -o clean"
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apply (tactic {* best_tac (lazy_cs add_safes (@{thms changeI} @ @{thms load1I} @ @{thms washI} @ @{thms dryI})) 1 *})
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done
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end
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