93 lines
2.8 KiB
Text
93 lines
2.8 KiB
Text
axiom testSorry : α
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opaque a : Nat
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opaque b : Nat
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def c := a
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@[irreducible] def d := a
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opaque P : Nat → Prop
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@[irreducible] def ac := a = c
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/--
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error: Not a definitional equality: the left-hand side
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a
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is not definitionally equal to the right-hand side
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b
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-/
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#guard_msgs in
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@[defeq] theorem a_eq_b : a = b := testSorry
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theorem a_eq_c : a = c := rfl
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@[defeq] theorem a_eq_c' : a = c := Eq.refl _
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theorem a_eq_c'' : a = c := Eq.refl _
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@[defeq] theorem a_eq_c''' : ac := by with_unfolding_all rfl
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@[defeq] theorem a_eq_d : a = d := by simp [d]
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/-- error: Not a definitional equality: the conclusion should be an equality, but is True -/
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#guard_msgs in
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@[defeq] def not_an_eq : True := trivial
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def Tricky.rfl := a_eq_b
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/--
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error: Not a definitional equality: the left-hand side
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a
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is not definitionally equal to the right-hand side
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b
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-/
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#guard_msgs in
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theorem Tricky.a_eq_b : a = b := rfl -- to confuse the heuristics
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/-! Does `#print` show the attribute? -/
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/-- info: @[defeq] theorem a_eq_c : a = c -/
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#guard_msgs in
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#print sig a_eq_c
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/-! Does dsimp use it? -/
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/-- error: dsimp made no progress -/
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#guard_msgs in example (h : P b) : P a := by dsimp [a_eq_b]; exact h
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/-- error: dsimp made no progress -/
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#guard_msgs in example (h : P b) : P a := by dsimp [Tricky.a_eq_b]; exact h
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#guard_msgs in example (h : P c) : P a := by dsimp [a_eq_c]; exact h
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#guard_msgs in example (h : P c) : P a := by dsimp [a_eq_c']; exact h
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/-- error: dsimp made no progress -/
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#guard_msgs in example (h : P c) : P a := by dsimp [a_eq_c'']; exact h
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-- a_eq_c''' is correctly tagged, but not used by `a_eq_c` because simp does not look through `ac`.
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/-- error: dsimp made no progress -/
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#guard_msgs in example (h : P c) : P a := by dsimp [a_eq_c''']; exact h
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#guard_msgs in example (h : P d) : P a := by dsimp [a_eq_d]; exact h
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-- Order of simp and rfl attribute
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def e1 := a
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@[simp] theorem e1_eq_a : e1 = a := rfl
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#guard_msgs in example (h : P a) : P e1 := by dsimp; exact h
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def e2 := a
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@[defeq,simp] theorem e2_eq_a : e2 = a := (rfl)
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#guard_msgs in example (h : P a) : P e2 := by dsimp; exact h
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def e3 := a
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@[simp,defeq] theorem e3_eq_a : e2 = a := (rfl) -- defeq has to come before simp
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/-- error: dsimp made no progress -/
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#guard_msgs in example (h : P a) : P e3 := by dsimp; exact h
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-- Tests the `defeq` attribute on a realized constant: That they are set, and that they
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-- are transported out
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def f := a
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#guard_msgs in example (h : P a) : P f := by dsimp [f]; exact h
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#guard_msgs in example (h : P a) : P f := by dsimp [f.eq_1]; exact h
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#guard_msgs in example (h : P a) : P f := by dsimp [f.eq_def]; exact h
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#guard_msgs in example (h : P a) : P f := by dsimp [f.eq_unfold]; exact h
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def Q := 1 = 1
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@[defeq, simp] theorem Q_true : Q := rfl
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/-- error: dsimp made no progress -/
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#guard_msgs in example : Q := by dsimp [Q_true]
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