26 lines
727 B
Text
26 lines
727 B
Text
variables {a b c : Prop}
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theorem ex1 (Ha : a) (Hab : a → b) (Hbc : b → c) : c :=
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suffices b from Hbc this
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suffices a from Hab this
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Ha
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theorem ex2 (Ha : a) (Hab : a → b) (Hbc : b → c) : c :=
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suffices b by apply Hbc; assumption
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suffices a by apply Hab; exact this
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Ha
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theorem ex3 (Ha : a) (Hab : a → b) (Hbc : b → c) : c := by
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suffices b by apply Hbc; assumption
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suffices a by apply Hab; assumption
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assumption
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theorem ex4 (Ha : a) (Hab : a → b) (Hbc : b → c) : c :=
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suffices h1 : b from Hbc h1
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suffices h2 : a from Hab h2
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Ha
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theorem ex5 (Ha : a) (Hab : a → b) (Hbc : b → c) : c := by
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suffices h1 : b by apply Hbc; assumption
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suffices h2 : a by apply Hab; exact h2
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assumption
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