31 lines
690 B
Text
31 lines
690 B
Text
variable {R M : Type}
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/-- Typeclass for the `⊥` (`\bot`) notation -/
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class Bot (α : Type) where
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/-- The bot (`⊥`, `\bot`) element -/
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bot : α
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/-- The bot (`⊥`, `\bot`) element -/
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notation "⊥" => Bot.bot
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structure Submodule (R : Type) (M : Type) [Zero M] [SMul R M] where
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carrier : M → Prop
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zero_mem : carrier (0 : M)
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variable [Zero M] [SMul R M]
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instance : Bot (Submodule R M) where
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bot := ⟨(· = 0), rfl⟩
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instance : Zero (Submodule R M) where
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zero := ⊥
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@[simp]
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theorem zero_eq_bot : (0 : Submodule R M) = ⊥ :=
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rfl
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theorem ohai : (0 : Submodule R M) = ⊥ := by
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simp -- works
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theorem oops : (0 : Submodule R M) = ⊥ := by
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dsimp -- should work
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