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88 lines
2.1 KiB
Plaintext
88 lines
2.1 KiB
Plaintext
import GameServer.Commands
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/-! ## Definitions -/
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DefinitionDoc Even as "Even"
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"
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`even n` ist definiert als `∃ r, a = 2 * r`.
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Die Definition kann man mit `unfold even at *` einsetzen.
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## Eigenschaften
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* Mathlib Doc: [#Even](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Parity.html#Even)"
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DefinitionDoc Odd as "Odd"
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"
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`odd n` ist definiert als `∃ r, a = 2 * r + 1`.
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Die Definition kann man mit `unfold odd at *` einsetzen.
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* Mathlib Doc: [Odd](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/Parity.html#Odd)"
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DefinitionDoc Injective as "Injective"
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"
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`Injective f` ist definiert als
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```
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∀ a b, f a = f b → a = b
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```
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definiert.
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* Mathlib Doc: [Injective](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.Injective)"
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DefinitionDoc Surjective as "Surjective"
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"
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`Surjective f` ist definiert als
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```
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∀ a, (∃ b, f a = b)
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```
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* Mathlib Doc: [Surjective](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.Surjective)"
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DefinitionDoc Bijective as "Bijective"
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"
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## Eigenschaften
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* Mathlib Doc: [#Bijective](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.Bijective)
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"
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DefinitionDoc LeftInverse as "LeftInverse"
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"
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## Eigenschaften
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* Mathlib Doc: [#LeftInverse](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Function.html#Function.LeftInverse)
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"
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DefinitionDoc RightInverse as "RightInverse"
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"
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## Eigenschaften
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* Mathlib Doc: [#RightInverse](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Init/Logic.html#RightInverse)
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"
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DefinitionDoc StrictMono as "StrictMono"
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"
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`StrictMono f` ist definiert als
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```
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∀ a b, a < b → f a < f b
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```
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## Eigenschaften
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* Mathlib Doc: [#StrictMono](https://leanprover-community.github.io/mathlib4_docs/Mathlib/Order/Monotone/Basic.html#StrictMono)
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"
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DefinitionDoc Symbol.Subset as "⊆" "
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Auf Mengen (`Set`) ist `A ⊆ B` als `∀x, x ∈ A → x ∈ B` implementiert.
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"
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DefinitionDoc Set.Nonempty as "Nonempty" "
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`A.Nonemty` ist als `∃ x, x ∈ A` definiert.
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"
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