31 lines
868 B
Plaintext
31 lines
868 B
Plaintext
(*
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* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*)
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theory Sep_MP_Example
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imports Sep_MP
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begin
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lemma "((P \<and>* Q \<and>* R \<longrightarrow>* B) \<and>* P \<and>* A \<and>* R \<and>* Q) s \<Longrightarrow> (A \<and>* B) s"
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(* sep_mp attempts to solve goals that could be solved by careful use of the sep_mp theorem *)
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apply (sep_mp)
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apply (clarsimp simp: sep_conj_ac)
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done
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(* Sep_mp uses the sep_cancel set to solve goals *)
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axiomatization
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Moo :: "'a :: stronger_sep_algebra => bool" and
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Bar :: "'a :: stronger_sep_algebra => bool"
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where Moo_Bar[sep_cancel] : "Moo s \<Longrightarrow> Bar s"
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lemma "((Bar \<and>* Q \<and>* R \<longrightarrow>* B) \<and>* Moo \<and>* A \<and>* R \<and>* Q) s \<Longrightarrow> (A \<and>* B) s"
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apply (sep_mp)
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apply (clarsimp simp: sep_conj_ac)
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done
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end
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