78 lines
1.4 KiB
Text
78 lines
1.4 KiB
Text
def f : nat → nat
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| 0 := 10
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| (n+1) := 20 + n
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open list tactic
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local attribute [-simp] map head
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example (a b c : nat) : head (map f [1, 2, 3]) = 20 :=
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begin
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dsimp [map],
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guard_target head [f 1, f 2, f 3] = 20,
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dsimp [f],
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guard_target head [20 + 0, 20 + 1, 20 + 2] = 20,
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dsimp [head],
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guard_target 20 + 0 = 20,
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reflexivity
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end
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example (a b c : nat) : head (map f [1, 2, 3]) = 20 :=
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begin
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dsimp [map, f, head],
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guard_target 20 + 0 = 20,
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reflexivity
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end
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@[simp] lemma succ_zero_eq_one : nat.succ 0 = 1 :=
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rfl
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def g : nat × nat → nat
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| (a, b) := a + b
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lemma gax (x y) : g (x, y) = x + y :=
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rfl
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attribute [simp] gax
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example (a b c : nat) : g (f 1, f 2) = 41 :=
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begin
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dsimp,
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guard_target f 1 + f 2 = 41,
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dsimp [f],
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reflexivity
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end
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example (a b c : nat) : g (f 1, f 2) = 41 :=
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begin
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dsimp [f],
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guard_target 20 + 0 + (20 + 1) = 41,
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reflexivity
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end
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example (a b c : nat) : g (f 1, f 2) = 41 :=
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begin
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dsimp [f] without gax,
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guard_target g (20 + 0, 20 + 1) = 41,
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dsimp [g],
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guard_target 20 + 0 + (20 + 1) = 41,
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reflexivity
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end
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local attribute [-simp] gax
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example (a b c : nat) : g (f 1, f 2) = 41 :=
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begin
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dsimp [f],
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guard_target g (20 + 0, 20 + 1) = 41,
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dsimp [gax],
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guard_target 20 + 0 + (20 + 1) = 41,
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reflexivity
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end
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example (a b c : nat) : g (f 1, f 2) = 41 :=
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begin
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dsimp [f, gax],
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guard_target 20 + 0 + (20 + 1) = 41,
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reflexivity
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end
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