30 lines
1.1 KiB
Text
30 lines
1.1 KiB
Text
import data.nat
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open - [simps] nat
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definition Sum : nat → (nat → nat) → nat :=
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sorry
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notation `Σ` binders ` < ` n `, ` r:(scoped f, Sum n f) := r
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lemma Sum_const [simp] (n : nat) (c : nat) : (Σ x < n, c) = n * c :=
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sorry
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lemma Sum_add [simp] (f g : nat → nat) (n : nat) : (Σ x < n, f x + g x) = (Σ x < n, f x) + (Σ x < n, g x) :=
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sorry
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attribute add.assoc add.comm add.left_comm mul_one add_zero zero_add one_mul mul.comm mul.assoc mul.left_comm [simp]
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example (f : nat → nat) (n : nat) : (Σ x < n, f x + 1) = (Σ x < n, f x) + n :=
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by simp
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example (f g h : nat → nat) (n : nat) : (Σ x < n, f x + g x + h x) = (Σ x < n, h x) + (Σ x < n, f x) + (Σ x < n, g x) :=
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by simp
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example (f g h : nat → nat) (n : nat) : (Σ x < n, f x + g x + h x) = Sum n h + (Σ x < n, f x) + (Σ x < n, g x) :=
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by simp
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example (f g h : nat → nat) (n : nat) : (Σ x < n, f x + g x + h x + 0) = Sum n h + (Σ x < n, f x) + (Σ x < n, g x) :=
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by simp
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example (f g h : nat → nat) (n : nat) : (Σ x < n, f x + g x + h x + 2) = 0 + Sum n h + (Σ x < n, f x) + (Σ x < n, g x) + 2 * n :=
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by simp
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