63 lines
1.7 KiB
Text
63 lines
1.7 KiB
Text
inductive Weekday where
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| sunday : Weekday
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| monday : Weekday
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| tuesday : Weekday
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| wednesday : Weekday
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| thursday : Weekday
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| friday : Weekday
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| saturday : Weekday
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def Weekday.next : Weekday -> Weekday :=
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fun d => match d with
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| sunday => monday
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| monday => tuesday
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| tuesday => wednesday
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| wednesday => thursday
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| thursday => friday
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| friday => saturday
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| saturday => sunday
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def Weekday.previous : Weekday -> Weekday
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| sunday => saturday
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| monday => sunday
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| tuesday => monday
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| wednesday => tuesday
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| thursday => wednesday
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| friday => thursday
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| saturday => friday
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theorem Weekday.nextOfPrevious (d : Weekday) : next (previous d) = d := by
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cases d
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all_goals rfl
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theorem Weekday.nextOfPrevious' (d : Weekday) : previous (next d) = d ∧ next (previous d) = d := by
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apply And.intro
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cases d <;> rfl
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cases d <;> rfl
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theorem Weekday.nextOfPrevious'' (d : Weekday) : previous (next d) = d ∧ next (previous d) = d := by
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apply And.intro <;> cases d <;> rfl
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open Lean.Parser.Tactic in
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macro "rwd " x:term : tactic => `(rw [$x:term]; done)
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theorem ex (a b c : α) (h₁ : a = b) (h₂ : a = c) : b = a ∧ c = a := by
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apply And.intro <;> first | rwd h₁ | rwd h₂
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theorem idEq (a : α) : id a = a :=
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rfl
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theorem Weekday.test (d : Weekday) : next (previous d) = id d := by
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cases d
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trace_state
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all_goals rw [idEq]
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trace_state
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all_goals rfl
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theorem Weekday.test2 (d : Weekday) : next (previous d) = id d := by
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cases d <;> rw [idEq]
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trace_state
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all_goals rfl
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def bug {a b c : Nat} (h₁ : a = b) (h₂ : b = c) : a = c := by
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apply Eq.trans <;> assumption
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