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(*
Example proof document for Isabelle/Isar Proof General.
$Id$
*)
theory Example imports Main begin
text {* Proper proof text -- \textit{naive version}. *}
theorem and_comms: "A & B --> B & A"
proof
assume "A & B"
then show "B & A"
proof
assume B and A
then show ?thesis ..
qed
qed
(* but on the other hand, who knows? *)
text {* Proper proof text -- \textit{advanced ve"rs"ion}. What do you think? Who knows. *}
theorem "B & A --> A & B"
proof
assume "B & A" -- "one of those kinds"
then obtain A and B ..
then show "A & B" ..
qed
(* foo bar wiggle *)
theorem "A & B --> B & A"
proof
assume "A & B"
then obtain B and A ..
then show "B & A" ..
qed
theorem "A & B --> B & A"
proof
assume "A & B"
then obtain B and A ..
then show "B & A" ..
qed
text {* Unstructured proof script. *}
theorem "A & B --> B & A" -- {* foo bar *}
apply (rule impI)
apply (erule conjE)
apply (rule conjI)
apply assumption
apply assumption
done
end
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