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feat(set_theory/game/basic): Add le_rfl on games (#13814)
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vihdzp committed May 3, 2022
1 parent 72816f9 commit b07c0f7
Showing 1 changed file with 4 additions and 2 deletions.
6 changes: 4 additions & 2 deletions src/set_theory/game/basic.lean
Expand Up @@ -57,8 +57,10 @@ instance : has_le game :=

-- Adding `@[refl]` and `@[trans]` attributes here would override the ones on
-- `preorder.le_refl` and `preorder.le_trans`, which breaks all non-`game` uses of `≤`!
theorem le_refl : ∀ x : game, x ≤ x :=
by { rintro ⟨x⟩, apply pgame.le_refl }
theorem le_rfl : ∀ {x : game}, x ≤ x :=
by { rintro ⟨x⟩, exact pgame.le_rfl }
theorem le_refl (x : game) : x ≤ x :=
le_rfl
theorem le_trans : ∀ x y z : game, x ≤ y → y ≤ z → x ≤ z :=
by { rintro ⟨x⟩ ⟨y⟩ ⟨z⟩, apply pgame.le_trans }
theorem le_antisymm : ∀ x y : game, x ≤ y → y ≤ x → x = y :=
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