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theory Example = Main:;
lemma I: "A --> A";
proof;
assume A;
show A; .;
qed;
lemma K: "A --> B --> A";
proof;
assume A;
show "B --> A";
proof;
show A; .;
qed;
qed;
lemma S: "(A --> B --> C) --> (A --> B) --> A --> C";
proof;
assume "A --> B --> C";
show "(A --> B) --> A --> C";
proof;
assume "A --> B";
show "A --> C";
proof;
assume A;
show C;
proof (rule mp);
show "B --> C"; by (rule mp);
show B; by (rule mp);
qed;
qed;
qed;
qed;
end;
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