17 lines
552 B
Text
17 lines
552 B
Text
--
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@[simp] theorem andTrue (p : Prop) : (p ∧ True) = p :=
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propext <| Iff.intro (fun ⟨h, _⟩ => h) (fun h => ⟨h, trivial⟩)
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attribute [simp] Nat.add_comm
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theorem ex1 (x : Nat) : (if x > 3 ∧ True then 1 else 2) = (if x > 3 then 1 else 2) :=
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by simp
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theorem ex2 (x : Nat) : (if x = 0 ∧ True then x + 1 else 2 + x) = (if x = 0 then 1 else x + 2) :=
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by simp (config := {contextual := true})
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#print ex2
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theorem ex3 (x : Nat) : (if h : x = 0 ∧ True then x + 1 else 2 + x) = (if h : x = 0 then 1 + x else x + 2) :=
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by simp
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#print ex3
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