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golf
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pitmonticone committed Sep 27, 2024
1 parent f81dd60 commit e5049ce
Showing 1 changed file with 3 additions and 5 deletions.
8 changes: 3 additions & 5 deletions equational_theories/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -164,9 +164,8 @@ theorem Equation7_implies_Equation41 (G: Type*) [Magma G] (h: Equation7 G) : Equ
theorem Equation41_implies_Equation40 (G: Type*) [Magma G] (h: Equation41 G) : Equation40 G :=
fun x y ↦ by rw [h x y y]

theorem Equation41_implies_Equation46 (G: Type*) [Magma G] (h: Equation41 G) : Equation46 G := by
intro x y z w
rwa [← h, h]
theorem Equation41_implies_Equation46 (G: Type*) [Magma G] (h: Equation41 G) : Equation46 G :=
fun _ _ _ _ ↦ by rwa [← h, h]

theorem Equation46_implies_Equation41 (G: Type*) [Magma G] (h: Equation46 G) : Equation41 G :=
fun _ _ _ => h _ _ _ _
Expand All @@ -188,8 +187,7 @@ theorem Equation387_implies_Equation43 (G: Type*) [Magma G] (h: Equation387 G) :
rw [← idem, ← h, idem]
have op_idem (x y : G) : (x ∘ x) ∘ (y ∘ y) = x ∘ y := by
rw [← h, ← h]
intro x y
rw [← op_idem, comm, op_idem]
exact fun _ _ ↦ by rw [← op_idem, comm, op_idem]

theorem Equation4513_implies_Equation4512 (G: Type*) [Magma G] (h: Equation4513 G) : Equation4512 G :=
fun _ _ _ ↦ h _ _ _ _
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