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remove trailing whitspace
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Mathlib/LinearAlgebra/TensorAlgebra/Hopf.lean

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -124,7 +124,7 @@ instance instHopfAlgebra : HopfAlgebra R T[M] where
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simp only [coe_coe, comul_apply, map_add, map_tmul, antipode_ι_apply, id_coe, id_eq,
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mul'_apply, mul_one, ← map_one (algebraMap R T[M]), antipode_algebraMap_apply]
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simp only [map_one, mul_one, one_mul, neg_add_cancel]
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| mul u v hu hv =>
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| mul u v hu hv =>
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conv =>
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rhs
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rw [convOne_apply, counit_mul, map_mul, ← convOne_apply, ← convOne_apply]
@@ -156,7 +156,7 @@ instance instHopfAlgebra : HopfAlgebra R T[M] where
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rw [LinearMap.lTensor, ← LinearMap.convMul_def, ← convOne_def]
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ext x
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induction x using induction with
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| algebraMap r =>
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| algebraMap r =>
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simp only [convMul_apply, comul_algebraMap, TensorProduct.algebraMap_apply, map_tmul,
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id_coe, id_eq, mul'_apply, convOne_apply, counit_algebraMap, ← map_one (algebraMap R
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T[M]), antipode_algebraMap_apply]
@@ -175,7 +175,7 @@ instance instHopfAlgebra : HopfAlgebra R T[M] where
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mul'_apply, mul_one, ← map_one (algebraMap R T[M]), antipode_algebraMap_apply]
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simp only [map_one, mul_one, one_mul, neg_add_cancel]
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abel_nf
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| mul u v hu hv =>
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| mul u v hu hv =>
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conv =>
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rhs
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rw [convOne_apply, counit_mul, map_mul, Algebra.commutes, ← convOne_apply,

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