lemma docs
This commit is contained in:
@@ -5,6 +5,8 @@ LemmaDoc not_not as "not_not" in "Logic"
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"
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"
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`not_not {A : Prop} : ¬¬A ↔ A`
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`not_not {A : Prop} : ¬¬A ↔ A`
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## Eigenschaften
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* `simp`-Lemma: Ja
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* `simp`-Lemma: Ja
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* Namespace: `Classical`
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* Namespace: `Classical`
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* Minimal Import: `Std.Logic`
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* Minimal Import: `Std.Logic`
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@@ -16,6 +18,8 @@ LemmaDoc not_or_of_imp as "not_or_of_imp" in "Logic"
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"
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"
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`not_or_of_imp {A B : Prop} : (A → B) → ¬A ∨ B`
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`not_or_of_imp {A B : Prop} : (A → B) → ¬A ∨ B`
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## Eigenschaften
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* `simp`-Lemma: Nein
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* `simp`-Lemma: Nein
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.Logic.Basic`
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* Minimal Import: `Mathlib.Logic.Basic`
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@@ -27,6 +31,8 @@ LemmaDoc imp_iff_not_or as "imp_iff_not_or" in "Logic"
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"
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"
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`imp_iff_not_or {A B : Prop} : (A → B) ↔ (¬A ∨ B)`
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`imp_iff_not_or {A B : Prop} : (A → B) ↔ (¬A ∨ B)`
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## Eigenschaften
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* `simp`-Lemma: Nein
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* `simp`-Lemma: Nein
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.Logic.Basic`
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* Minimal Import: `Mathlib.Logic.Basic`
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@@ -51,6 +57,8 @@ LemmaDoc Nat.pos_iff_ne_zero as "pos_iff_ne_zero" in "Nat"
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"
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`Nat.pos_iff_ne_zero {n : ℕ} : 0 < n ↔ n ≠ 0`
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`Nat.pos_iff_ne_zero {n : ℕ} : 0 < n ↔ n ≠ 0`
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## Eigenschaften
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* `simp`-Lemma: Nein
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* `simp`-Lemma: Nein
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* Namespace: `Nat`
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* Namespace: `Nat`
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* Minimal Import: `Std.Data.Nat.Lemmas`
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* Minimal Import: `Std.Data.Nat.Lemmas`
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@@ -59,8 +67,10 @@ LemmaDoc Nat.pos_iff_ne_zero as "pos_iff_ne_zero" in "Nat"
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-- TODO: Not minimal description
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-- TODO: Not minimal description
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LemmaDoc zero_add as "zero_add" in "Addition"
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LemmaDoc zero_add as "zero_add" in "Addition"
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"zero_add (a : ℕ) : 0 + a = a`.
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"
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`zero_add (a : ℕ) : 0 + a = a`
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## Eigenschaften
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* `simp`-Lemma: Ja
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* `simp`-Lemma: Ja
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* Namespace: `-`
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* Namespace: `-`
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@@ -69,7 +79,10 @@ LemmaDoc zero_add as "zero_add" in "Addition"
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"
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LemmaDoc add_zero as "add_zero" in "Addition"
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LemmaDoc add_zero as "add_zero" in "Addition"
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"This lemma says `∀ a : ℕ, a + 0 = a`.
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"
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This lemma says `∀ a : ℕ, a + 0 = a`.
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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@@ -79,6 +92,8 @@ LemmaDoc add_zero as "add_zero" in "Addition"
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LemmaDoc add_succ as "add_succ" in "Addition"
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LemmaDoc add_succ as "add_succ" in "Addition"
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"This lemma says `∀ a b : ℕ, a + succ b = succ (a + b)`.
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"This lemma says `∀ a b : ℕ, a + succ b = succ (a + b)`.
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -88,6 +103,8 @@ LemmaDoc not_forall as "not_forall" in "Logic"
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"
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`not_forall {α : Sort _} {P : α → Prop} : ¬(∀ x, → P x) ↔ ∃ x, ¬P x`
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`not_forall {α : Sort _} {P : α → Prop} : ¬(∀ x, → P x) ↔ ∃ x, ¬P x`
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## Eigenschaften
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* `simp`-Lemma: Ja
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* `simp`-Lemma: Ja
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.Logic.Basic`
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* Minimal Import: `Mathlib.Logic.Basic`
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@@ -95,82 +112,139 @@ LemmaDoc not_forall as "not_forall" in "Logic"
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"
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LemmaDoc not_exists as "not_exists" in "Logic"
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LemmaDoc not_exists as "not_exists" in "Logic"
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"`∀ (A : Prop), ¬(∃ x, A) ↔ ∀x, (¬A)`.
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"
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`not_exists {α : Sort _} {P : α → Prop} : (¬∃ x, P x) ↔ ∀ (x : α), ¬P x.
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* `simp`-Lemma:
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## Eigenschaften
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* `simp`-Lemma: Ja
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Std.Logic`
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* Mathlib Doc: [#]()"
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* Mathlib Doc: [#not_exists](https://leanprover-community.github.io/mathlib4_docs/Std/Logic.html#not_exists)"
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LemmaDoc even_iff_not_odd as "even_iff_not_odd" in "Nat"
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LemmaDoc Nat.even_iff_not_odd as "even_iff_not_odd" in "Nat"
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"`Even n ↔ ¬ (Odd n)`
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"
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`even_iff_not_odd {n : ℕ} : Even n ↔ ¬Odd n`
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* `simp`-Lemma:
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## Eigenschaften
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Mathlib Doc: [#]()"
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LemmaDoc odd_iff_not_even as "odd_iff_not_even" in "Nat"
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* `simp`-Lemma: Nein
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"`Odd n ↔ ¬ (Even n)`
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* Namespace: `Nat`
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* Minimal Import: `Mathlib.Data.Nat.Parity`
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* Mathlib Doc: [#Nat.even_iff_not_odd](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Parity.html#Nat.even_iff_not_odd)"
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* `simp`-Lemma:
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LemmaDoc Nat.odd_iff_not_even as "odd_iff_not_even" in "Nat"
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* Namespace: `-`
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"
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* Minimal Import: `Mathlib.`
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`Nat.odd_iff_not_even {n : ℕ} : Odd n ↔ ¬Even n`
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* Mathlib Doc: [#]()"
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## Eigenschaften
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* `simp`-Lemma: Ja
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* Namespace: `Nat`
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* Minimal Import: `Mathlib.Data.Nat.Parity`
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* Mathlib Doc: [#Nat.odd_iff_not_even](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Nat/Parity.html#Nat.odd_iff_not_even)"
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LemmaDoc even_square as "even_square" in "Nat"
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LemmaDoc even_square as "even_square" in "Nat"
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"`∀ (n : ℕ), Even n → Even (n ^ 2)`
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"
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`even_square : (n : ℕ), Even n → Even (n ^ 2)`
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* `simp`-Lemma:
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## Eigenschaften
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* `simp`-Lemma: Nein
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* Mathlib Doc: [#]()
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* *Nicht in Mathlib*
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"
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LemmaDoc mem_univ as "mem_univ" in "Set"
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LemmaDoc Set.mem_univ as "mem_univ" in "Set"
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"x ∈ @univ α
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"
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`Set.mem_univ {α : Type _} (x : α) : x ∈ @univ α`
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* `simp`-Lemma:
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Jedes Element ist in `univ`, der Menge aller Elemente eines Typs `α`.
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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## Eigenschaften
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* Mathlib Doc: [#]()
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* `simp`-Lemma: Ja
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* Namespace: `Set`
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* Minimal Import: `Mathlib.Data.Set.Basic`
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* Mathlib Doc: [#mem_univ](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.mem_univ)
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"
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LemmaDoc not_mem_empty as "not_mem_empty" in "Set"
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LemmaDoc not_mem_empty as "not_mem_empty" in "Set"
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`Set.not_mem_empty {α : Type _} (x : α) : x ∉ ∅`
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* `simp`-Lemma:
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Kein Element ist in der leeren Menge.
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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## Eigenschaften
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* Mathlib Doc: [#]()
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* `simp`-Lemma: Nein
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* Namespace: `Set`
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* Minimal Import: `Mathlib.Data.Set.Basic`
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* Mathlib Doc: [#not_mem_empty](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.not_mem_empty)
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LemmaDoc empty_subset as "empty_subset" in "Set"
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LemmaDoc empty_subset as "empty_subset" in "Set"
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`Set.empty_subset {α : Type u} (s : Set α) : ∅ ⊆ s`
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* `simp`-Lemma:
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## Eigenschaften
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* `simp`-Lemma: Ja
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* Mathlib Doc: [#]()
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* Namespace: `Set`
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* Minimal Import: `Mathlib.Data.Set.Basic`
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* Mathlib Doc: [#empty_subset](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.empty_subset)
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LemmaDoc Subset.antisymm as "Subset.antisymm" in "Set"
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`Set.Subset.antisymm {α : Type u} {a : Set α} {b : Set α} (h₁ : a ⊆ b) (h₂ : b ⊆ a) : a = b`
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Zwei Mengen sind identisch, wenn sowohl $A \\subseteq B$ wie auch $B \\subseteq A$.
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## Details
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`apply Subset.antisymm` ist eine Möglichkeit Gleichungen von Mengen zu zeigen.
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eine andere ist `ext i`, welches Elementweise funktiniert.
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Siehe auch
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[`#Subset.antisymm_iff`](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm_iff)
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für die Iff-Version.
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## Eigenschaften
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* `simp`-Lemma: Nein
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* Namespace: `Set.Subset`
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* Minimal Import: `Mathlib.Data.Set.Basic`
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* Mathlib Doc: [#Subset.antisymm](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm)
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LemmaDoc Subset.antisymm_iff as "Subset.antisymm_iff" in "Set"
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LemmaDoc Subset.antisymm_iff as "Subset.antisymm_iff" in "Set"
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`Set.Subset.antisymm_iff {α : Type u} {a : Set α} {b : Set α} : a = b ↔ a ⊆ b ∧ b ⊆ a`
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* `simp`-Lemma:
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Zwei Mengen sind identisch, wenn sowohl $A \\subseteq B$ wie auch $B \\subseteq A$.
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* Namespace: `-`
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## Details
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* Minimal Import: `Mathlib.`
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* Mathlib Doc: [#]()
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`rw [Subset.antisymm_iff]` ist eine Möglichkeit Gleichungen von Mengen zu zeigen.
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eine andere ist `ext i`, welches Elementweise funktiniert.
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Siehe auch
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[`#Subset.antisymm`](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm)
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für eine verwandte Version.
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## Eigenschaften
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* `simp`-Lemma: Nein
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* Namespace: `Set.Subset`
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* Minimal Import: `Mathlib.Data.Set.Basic`
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* Mathlib Doc: [#Subset.antisymm_iff](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Data/Set/Basic.html#Set.Subset.antisymm_iff)
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LemmaDoc Nat.prime_def_lt'' as "Nat.prime_def_lt''" in "Nat"
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LemmaDoc Nat.prime_def_lt'' as "Nat.prime_def_lt''" in "Nat"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -181,6 +255,8 @@ LemmaDoc Nat.prime_def_lt'' as "Nat.prime_def_lt''" in "Nat"
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LemmaDoc Finset.sum_add_distrib as "Finset.sum_add_distrib" in "Sum"
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LemmaDoc Finset.sum_add_distrib as "Finset.sum_add_distrib" in "Sum"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -190,6 +266,8 @@ LemmaDoc Finset.sum_add_distrib as "Finset.sum_add_distrib" in "Sum"
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LemmaDoc Fin.sum_univ_castSucc as "Fin.sum_univ_castSucc" in "Sum"
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LemmaDoc Fin.sum_univ_castSucc as "Fin.sum_univ_castSucc" in "Sum"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -199,6 +277,8 @@ LemmaDoc Fin.sum_univ_castSucc as "Fin.sum_univ_castSucc" in "Sum"
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LemmaDoc Nat.succ_eq_add_one as "Nat.succ_eq_add_one" in "Sum"
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LemmaDoc Nat.succ_eq_add_one as "Nat.succ_eq_add_one" in "Sum"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -208,6 +288,8 @@ LemmaDoc Nat.succ_eq_add_one as "Nat.succ_eq_add_one" in "Sum"
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LemmaDoc Nat.zero_eq as "Nat.succ_eq_add_one" in "Sum"
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LemmaDoc Nat.zero_eq as "Nat.succ_eq_add_one" in "Sum"
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"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -217,6 +299,8 @@ LemmaDoc Nat.zero_eq as "Nat.succ_eq_add_one" in "Sum"
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LemmaDoc add_comm as "add_comm" in "Nat"
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LemmaDoc add_comm as "add_comm" in "Nat"
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"
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"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -226,6 +310,8 @@ LemmaDoc add_comm as "add_comm" in "Nat"
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LemmaDoc mul_add as "mul_add" in "Nat"
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LemmaDoc mul_add as "mul_add" in "Nat"
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"
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"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -235,6 +321,8 @@ LemmaDoc mul_add as "mul_add" in "Nat"
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LemmaDoc add_mul as "add_mul" in "Nat"
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LemmaDoc add_mul as "add_mul" in "Nat"
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"
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"
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## Eigenschaften
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* `simp`-Lemma:
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* `simp`-Lemma:
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* Namespace: `-`
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* Namespace: `-`
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* Minimal Import: `Mathlib.`
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* Minimal Import: `Mathlib.`
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@@ -244,6 +332,8 @@ LemmaDoc add_mul as "add_mul" in "Nat"
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LemmaDoc arithmetic_sum as "arithmetic_sum" in "Sum"
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LemmaDoc arithmetic_sum as "arithmetic_sum" in "Sum"
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"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -253,6 +343,8 @@ LemmaDoc arithmetic_sum as "arithmetic_sum" in "Sum"
|
|||||||
LemmaDoc add_pow_two as "add_pow_two" in "Nat"
|
LemmaDoc add_pow_two as "add_pow_two" in "Nat"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -262,6 +354,8 @@ LemmaDoc add_pow_two as "add_pow_two" in "Nat"
|
|||||||
LemmaDoc Finset.sum_comm as "Finset.sum_comm" in "Sum"
|
LemmaDoc Finset.sum_comm as "Finset.sum_comm" in "Sum"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -271,6 +365,8 @@ LemmaDoc Finset.sum_comm as "Finset.sum_comm" in "Sum"
|
|||||||
LemmaDoc Function.comp_apply as "Function.comp_apply" in "Function"
|
LemmaDoc Function.comp_apply as "Function.comp_apply" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -280,6 +376,8 @@ LemmaDoc Function.comp_apply as "Function.comp_apply" in "Function"
|
|||||||
LemmaDoc not_le as "not_le" in "Logic"
|
LemmaDoc not_le as "not_le" in "Logic"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -289,6 +387,8 @@ LemmaDoc not_le as "not_le" in "Logic"
|
|||||||
LemmaDoc if_pos as "if_pos" in "Logic"
|
LemmaDoc if_pos as "if_pos" in "Logic"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -298,6 +398,8 @@ LemmaDoc if_pos as "if_pos" in "Logic"
|
|||||||
LemmaDoc if_neg as "if_neg" in "Logic"
|
LemmaDoc if_neg as "if_neg" in "Logic"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -307,6 +409,8 @@ LemmaDoc if_neg as "if_neg" in "Logic"
|
|||||||
LemmaDoc StrictMono.injective as "StrictMono.injective" in "Function"
|
LemmaDoc StrictMono.injective as "StrictMono.injective" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -316,6 +420,8 @@ LemmaDoc StrictMono.injective as "StrictMono.injective" in "Function"
|
|||||||
LemmaDoc StrictMono.add as "StrictMono.add" in "Function"
|
LemmaDoc StrictMono.add as "StrictMono.add" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -325,6 +431,8 @@ LemmaDoc StrictMono.add as "StrictMono.add" in "Function"
|
|||||||
LemmaDoc Odd.strictMono_pow as "Odd.strictMono_pow" in "Function"
|
LemmaDoc Odd.strictMono_pow as "Odd.strictMono_pow" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -334,6 +442,8 @@ LemmaDoc Odd.strictMono_pow as "Odd.strictMono_pow" in "Function"
|
|||||||
LemmaDoc Exists.choose as "Exists.choose" in "Function"
|
LemmaDoc Exists.choose as "Exists.choose" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -343,6 +453,8 @@ LemmaDoc Exists.choose as "Exists.choose" in "Function"
|
|||||||
LemmaDoc Exists.choose_spec as "Exists.choose_spec" in "Function"
|
LemmaDoc Exists.choose_spec as "Exists.choose_spec" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -351,6 +463,8 @@ LemmaDoc Exists.choose_spec as "Exists.choose_spec" in "Function"
|
|||||||
LemmaDoc congrArg as "congrArg" in "Function"
|
LemmaDoc congrArg as "congrArg" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -359,6 +473,8 @@ LemmaDoc congrArg as "congrArg" in "Function"
|
|||||||
LemmaDoc congrFun as "congrFun" in "Function"
|
LemmaDoc congrFun as "congrFun" in "Function"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -368,6 +484,8 @@ LemmaDoc congrFun as "congrFun" in "Function"
|
|||||||
LemmaDoc Iff.symm as "Iff.symm" in "Logic"
|
LemmaDoc Iff.symm as "Iff.symm" in "Logic"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -382,6 +500,8 @@ DefinitionDoc Even as "Even"
|
|||||||
"
|
"
|
||||||
`even n` ist definiert als `∃ r, a = 2 * r`.
|
`even n` ist definiert als `∃ r, a = 2 * r`.
|
||||||
Die Definition kann man mit `unfold even at *` einsetzen.
|
Die Definition kann man mit `unfold even at *` einsetzen.
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -415,6 +535,8 @@ DefinitionDoc Surjective as "Surjective"
|
|||||||
DefinitionDoc Bijective as "Bijective"
|
DefinitionDoc Bijective as "Bijective"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -424,6 +546,8 @@ DefinitionDoc Bijective as "Bijective"
|
|||||||
DefinitionDoc LeftInverse as "LeftInverse"
|
DefinitionDoc LeftInverse as "LeftInverse"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
@@ -433,6 +557,8 @@ DefinitionDoc LeftInverse as "LeftInverse"
|
|||||||
DefinitionDoc RightInverse as "RightInverse"
|
DefinitionDoc RightInverse as "RightInverse"
|
||||||
"
|
"
|
||||||
|
|
||||||
|
## Eigenschaften
|
||||||
|
|
||||||
* `simp`-Lemma:
|
* `simp`-Lemma:
|
||||||
* Namespace: `-`
|
* Namespace: `-`
|
||||||
* Minimal Import: `Mathlib.`
|
* Minimal Import: `Mathlib.`
|
||||||
|
|||||||
@@ -106,4 +106,4 @@ ist deine!
|
|||||||
"
|
"
|
||||||
|
|
||||||
NewTactic push_neg
|
NewTactic push_neg
|
||||||
NewLemma even_iff_not_odd odd_iff_not_even not_exists not_forall
|
NewLemma Nat.even_iff_not_odd Nat.odd_iff_not_even not_exists not_forall
|
||||||
|
|||||||
@@ -26,7 +26,7 @@ Statement not_mem_empty "" {A : Type} (x : A) :
|
|||||||
**Robo**: Dann behaupte das doch."
|
**Robo**: Dann behaupte das doch."
|
||||||
tauto
|
tauto
|
||||||
|
|
||||||
NewLemma mem_univ
|
NewLemma Set.mem_univ
|
||||||
|
|
||||||
Conclusion "Der Junge rennt weiter.
|
Conclusion "Der Junge rennt weiter.
|
||||||
|
|
||||||
|
|||||||
@@ -52,8 +52,7 @@ Statement subset_empty_iff {A : Type _} (s : Set A) :
|
|||||||
|
|
||||||
constructor
|
constructor
|
||||||
intro h
|
intro h
|
||||||
rw [Subset.antisymm_iff]
|
apply Subset.antisymm
|
||||||
constructor
|
|
||||||
assumption
|
assumption
|
||||||
simp only [empty_subset]
|
simp only [empty_subset]
|
||||||
intro a
|
intro a
|
||||||
@@ -63,6 +62,6 @@ Statement subset_empty_iff {A : Type _} (s : Set A) :
|
|||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
NewLemma Subset.antisymm empty_subset
|
||||||
|
|
||||||
end MySet
|
end MySet
|
||||||
|
|||||||
@@ -47,6 +47,4 @@ Statement eq_empty_iff_forall_not_mem
|
|||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|
||||||
end MySet
|
end MySet
|
||||||
|
|||||||
@@ -31,5 +31,3 @@ Statement nonempty_iff_ne_empty
|
|||||||
rfl
|
rfl
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -27,5 +27,3 @@ Statement
|
|||||||
simp
|
simp
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -31,5 +31,3 @@ Statement
|
|||||||
rw [univ_union]
|
rw [univ_union]
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -31,5 +31,3 @@ Statement
|
|||||||
exact h4
|
exact h4
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -34,5 +34,3 @@ Statement
|
|||||||
exact hx
|
exact hx
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -33,5 +33,3 @@ Statement
|
|||||||
rfl
|
rfl
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -33,5 +33,3 @@ Statement
|
|||||||
ring
|
ring
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -38,5 +38,3 @@ Statement
|
|||||||
|
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -37,5 +37,3 @@ Statement
|
|||||||
|
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -35,5 +35,3 @@ Statement
|
|||||||
|
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -29,5 +29,3 @@ Statement
|
|||||||
library_search
|
library_search
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -24,5 +24,3 @@ Statement
|
|||||||
ring
|
ring
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -23,5 +23,3 @@ Statement
|
|||||||
"" : True := sorry
|
"" : True := sorry
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
@@ -24,5 +24,3 @@ Statement
|
|||||||
ring
|
ring
|
||||||
|
|
||||||
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
NewTactic constructor intro rw assumption rcases simp tauto trivial
|
||||||
|
|
||||||
NewLemma Subset.antisymm_iff empty_subset
|
|
||||||
|
|||||||
Reference in New Issue
Block a user