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feat(analysis/normed_space/linear_isometry): symm_trans (#11892)
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Add a `simp` lemma `linear_isometry_equiv.symm_trans`, like
`coe_symm_trans` but without a coercion involved.  `coe_symm_trans`
can then be proved by `simp`, so stops being a `simp` lemma itself.
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jsm28 committed Feb 7, 2022
1 parent b1b09eb commit 3c70566
Showing 1 changed file with 5 additions and 1 deletion.
6 changes: 5 additions & 1 deletion src/analysis/normed_space/linear_isometry.lean
Expand Up @@ -411,7 +411,11 @@ omit σ₁₃ σ₂₁ σ₃₁ σ₃₂
@[simp] lemma self_comp_symm : e ∘ e.symm = id := e.symm.symm_comp_self

include σ₁₃ σ₂₁ σ₃₂ σ₃₁
@[simp] lemma coe_symm_trans (e₁ : E ≃ₛₗᵢ[σ₁₂] E₂) (e₂ : E₂ ≃ₛₗᵢ[σ₂₃] E₃) :
@[simp] lemma symm_trans (e₁ : E ≃ₛₗᵢ[σ₁₂] E₂) (e₂ : E₂ ≃ₛₗᵢ[σ₂₃] E₃) :
(e₁.trans e₂).symm = e₂.symm.trans e₁.symm :=
rfl

lemma coe_symm_trans (e₁ : E ≃ₛₗᵢ[σ₁₂] E₂) (e₂ : E₂ ≃ₛₗᵢ[σ₂₃] E₃) :
⇑(e₁.trans e₂).symm = e₁.symm ∘ e₂.symm :=
rfl

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