cf36ac986d
This PR optimizes the construction on congruence proofs in `simp`. It uses some of the ideas used in `Sym.simp`.
40 lines
1.1 KiB
Text
40 lines
1.1 KiB
Text
def f {α} (a b : α) := a
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theorem f_Eq {α} (a b : α) : f a b = a :=
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rfl
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theorem ex1 (a b c : α) : f (f a b) c = a := by
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simp -implicitDefEqProofs [f_Eq]
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/--
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info: theorem ex1.{u_1} : ∀ {α : Sort u_1} (a b c : α), f (f a b) c = a :=
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fun {α} a b c =>
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of_eq_true
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(Eq.trans (congrFun' (congrArg Eq (Eq.trans (congrFun' (congrArg f (f_Eq a b)) c) (f_Eq a c))) a) (eq_self a))
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-/
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#guard_msgs in
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#print ex1
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theorem ex1' (a b c : α) : f (f a b) c = a := by
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simp +implicitDefEqProofs [f_Eq]
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/--
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info: theorem ex1'.{u_1} : ∀ {α : Sort u_1} (a b c : α), f (f a b) c = a :=
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fun {α} a b c => of_eq_true (eq_self a)
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-/
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#guard_msgs in
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#print ex1'
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theorem ex2 (p : Nat → Bool) (x : Nat) (h : p x = true) : (if p x then 1 else 2) = 1 := by
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simp [h]
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/--
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info: theorem ex2 : ∀ (p : Nat → Bool) (x : Nat), p x = true → (if p x = true then 1 else 2) = 1 :=
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fun p x h =>
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of_eq_true
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(Eq.trans
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(congrFun' (congrArg Eq (ite_cond_eq_true 1 2 (Eq.trans (congrFun' (congrArg Eq h) true) (eq_self true)))) 1)
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(eq_self 1))
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-/
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#guard_msgs in
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#print ex2
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