cf36ac986d
This PR optimizes the construction on congruence proofs in `simp`. It uses some of the ideas used in `Sym.simp`.
47 lines
1.2 KiB
Text
47 lines
1.2 KiB
Text
theorem ex1 (a : α) (b : List α) : (a::b = []) = False :=
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by simp
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theorem ex2 (a : α) (b : List α) : (a::b = []) = False :=
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by simp
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theorem ex3 (x : Nat) : (if Nat.succ x = 0 then 1 else 2) = 2 :=
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by simp
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theorem ex4 (x : Nat) : (if 10 = 0 then 1 else 2) = 2 :=
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by simp
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theorem ex5 : (10 = 20) = False :=
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by simp
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/--
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info: theorem ex5 : (10 = 20) = False :=
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of_eq_true (Eq.trans (congrFun' (congrArg Eq (eq_false_of_decide (Eq.refl false))) False) (eq_self False))
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-/
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#guard_msgs in
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#print ex5
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theorem ex6 : (if "hello" = "world" then 1 else 2) = 2 :=
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by simp (config := { decide := true })
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/--
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info: theorem ex6 : (if "hello" = "world" then 1 else 2) = 2 :=
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of_eq_true (eq_true_of_decide (Eq.refl true))
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-/
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#guard_msgs in
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#print ex6
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theorem ex7 : (if "hello" = "world" then 1 else 2) = 2 := by
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simp (config := { decide := false }) [-String.reduceEq]
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guard_target =ₛ ¬ "hello" = "world"
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fail_if_success simp [-String.reduceEq]
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simp (config := { decide := true }) [-String.reduceEq]
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theorem ex8 : (10 + 2000 = 20) = False :=
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by simp
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def fact : Nat → Nat
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| 0 => 1
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| x+1 => (x+1) * fact x
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theorem ex9 : (if fact 100 > 10 then true else false) = true :=
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by simp (config := { decide := true })
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