document - Isabelle

proof (unfold Ex-def )assume c: ∀ C . (∀ x. P x −→ C ) −→ Cassume r: ∧ x. P x =⇒ Cfrom c have (∀ x. P x −→ C ) −→ C ..also have ∀ x. P x −→ Cprooffix x show P x −→ Cproofassume P xthen show C by (rule r)qedqedfinally show C .qed2.2 Classical logiclocale classical =assumes classical: (¬ A =⇒ A) =⇒ Atheorem (in classical)Peirce ′ s-Law: ((A −→ B) −→ A) −→ Aproofassume a: (A −→ B) −→ Ashow Aproof (rule classical)assume ¬ Ahave A −→ Bproofassume Awith 〈 ¬ A 〉 show B by (rule contradiction)qedwith a show A ..qedqedtheorem (in classical)double-negation: ¬ ¬ A =⇒ Aproof −assume ¬ ¬ Ashow Aproof (rule classical)assume ¬ Awith 〈 ¬ ¬ A 〉 show ?thesis by (rule contradiction)qedqedtheorem (in classical)tertium-non-datur: A ∨ ¬ A21