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chore(GroupTheory): golf entire base_smul_def and summand_smul_def using rfl (leanprover-community#28563)
Co-authored-by: euprunin <euprunin@users.noreply.github.com>
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Mathlib/GroupTheory/PushoutI.lean

Lines changed: 2 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -466,18 +466,12 @@ noncomputable instance mulAction : MulAction (PushoutI φ) (NormalWord d) :=
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smul_inv_smul, base_smul_def', MonoidHom.apply_ofInjective_symm]
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theorem base_smul_def (h : H) (w : NormalWord d) :
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base φ h • w = { w with head := h * w.head } := by
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dsimp [NormalWord.mulAction, instHSMul, SMul.smul]
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rw [lift_base]
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rfl
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base φ h • w = { w with head := h * w.head } := rfl
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theorem summand_smul_def {i : ι} (g : G i) (w : NormalWord d) :
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of (φ := φ) i g • w = (equivPair i).symm
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{ equivPair i w with
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head := g * (equivPair i w).head } := by
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dsimp [NormalWord.mulAction, instHSMul, SMul.smul]
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rw [lift_of]
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rfl
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head := g * (equivPair i w).head } := rfl
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theorem of_smul_eq_smul {i : ι} (g : G i) (w : NormalWord d) :
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of (φ := φ) i g • w = g • w := by

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