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