7c4284aa91
Despite what it said in its docstring, `simpMatchWF?` seems to behave like `simpMatch?`, so let’s just use that.
132 lines
2.5 KiB
Text
132 lines
2.5 KiB
Text
-- `g.eq_def` is not reserved yet
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theorem g.eq_def : 1 + x = x + 1 := Nat.add_comm ..
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/--
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error: failed to declare `g` because `g.eq_def` has already been declared
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-/
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#guard_msgs (error) in
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def g (x : Nat) := x + 1
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def f (x : Nat) := x + 1
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/--
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error: 'f.eq_def' is a reserved name
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-/
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#guard_msgs (error) in
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theorem f.eq_def : f x = x + 1 := rfl
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/--
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error: 'f.eq_1' is a reserved name
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-/
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#guard_msgs (error) in
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theorem f.eq_1 : f x = x + 1 := rfl
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def f.eq_2_ := 10 -- Should be ok
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/-- info: f.eq_1 (x : Nat) : f x = x + 1 -/
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#guard_msgs in
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#check f.eq_1
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/-- error: unknown identifier 'f.eq_2' -/
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#guard_msgs (error) in
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#check f.eq_2
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/-- info: f.eq_def (x : Nat) : f x = x + 1 -/
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#guard_msgs in
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#check f.eq_def
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def nonrecfun : Bool → Nat
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| false => 0
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| true => 0
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/--
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info: nonrecfun.eq_def :
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∀ (x : Bool),
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nonrecfun x =
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match x with
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| false => 0
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| true => 0
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-/
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#guard_msgs in
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#check nonrecfun.eq_def
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/--
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info: nonrecfun.eq_1 :
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∀ (x : Bool),
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nonrecfun x =
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match x with
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| false => 0
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| true => 0
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-/
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#guard_msgs in
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#check nonrecfun.eq_1
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def fact : Nat → Nat
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| 0 => 1
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| n+1 => (n+1) * fact n
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/--
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info: fact.eq_def :
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∀ (x : Nat),
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fact x =
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match x with
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| 0 => 1
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| n.succ => (n + 1) * fact n
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-/
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#guard_msgs in
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#check fact.eq_def
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/-- info: fact.eq_1 : fact 0 = 1 -/
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#guard_msgs in
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#check fact.eq_1
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/-- info: fact.eq_2 (n : Nat) : fact n.succ = (n + 1) * fact n -/
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#guard_msgs in
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#check fact.eq_2
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/-- error: unknown identifier 'fact.eq_3' -/
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#guard_msgs (error) in
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#check fact.eq_3
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def fact' : Nat → Nat
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| 0 => 1
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| n+1 => (n+1) * fact' n
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example : fact' 0 + fact' 0 = 2 := by
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simp [fact'.eq_1]
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example : fact' 0 + fact' 1 = 2 := by
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rw [fact'.eq_1]
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guard_target =ₛ 1 + fact' 1 = 2
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rw [fact'.eq_2]
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guard_target =ₛ 1 + (0+1) * fact' 0 = 2
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rw [fact'.eq_1]
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example : fact' 0 + fact' 1 = 2 := by
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rw [fact'.eq_def, fact'.eq_def]; simp
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guard_target =ₛ 1 + fact' 0 = 2
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rw [fact'.eq_def]
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guard_target =
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(1 + fact.match_1 (fun _ => Nat) 0 (fun _ => 1) fun n => (n + 1) * fact' n) = 2
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simp
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theorem bla : 0 = 0 := rfl
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def bla.def := 1 -- should work since `bla` is a theorem
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def bla.eq_1 := 2 -- should work since `bla` is a theorem
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def find (as : Array Int) (i : Nat) (v : Int) : Nat :=
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if _ : i < as.size then
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if as[i] = v then
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i
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else
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find as (i+1) v
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else
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i
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/--
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info: find.eq_def (as : Array Int) (i : Nat) (v : Int) :
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find as i v = if x : i < as.size then if as[i] = v then i else find as (i + 1) v else i
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-/
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#guard_msgs in
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#check find.eq_def
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