5a34ffb9b0
This PR upstreams much of the material from `Mathlib/Data/Nat/Init.lean` and `Mathlib/Data/Nat/Basic.lean`.
25 lines
619 B
Text
25 lines
619 B
Text
def f (x : Nat) := x + 1
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theorem f_eq (x : Nat) : f (x + 1) = x + 2 := rfl
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theorem ex1 : f (f (x + 1)) = x + 3 := by
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simp -implicitDefEqProofs only [f_eq]
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/--
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info: theorem ex1 : ∀ {x : Nat}, f (f (x + 1)) = x + 3 :=
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fun {x} =>
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of_eq_true
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(Eq.trans (congrArg (fun x_1 => x_1 = x + 3) (Eq.trans (congrArg f (f_eq x)) (f_eq (x + 1)))) (eq_self (x + 1 + 2)))
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-/
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#guard_msgs in
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#print ex1
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theorem ex2 : f (f (x + 1)) = x + 3 := by
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simp +implicitDefEqProofs only [f_eq]
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/--
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info: theorem ex2 : ∀ {x : Nat}, f (f (x + 1)) = x + 3 :=
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fun {x} => of_eq_true (eq_self (x + 1 + 2))
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-/
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#guard_msgs in
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#print ex2
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