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[Merged by Bors] - chore(RingTheory/Polynomial/Basic): squeeze terminal simps #40833

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[Merged by Bors] - chore(RingTheory/Polynomial/Basic): squeeze terminal simps #40833

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13 changes: 2 additions & 11 deletions Mathlib/RingTheory/Polynomial/Basic.lean
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Expand Up @@ -763,17 +763,8 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
(renameEquiv R <| (Equiv.sumComm (↥sᶜ) s).trans <| Equiv.Set.sumCompl s)
have : (rename (↑)).toRingHom = eqv.toAlgHom.toRingHom.comp C := by
apply ringHom_ext
· intro
simp only [eqv, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, rename_C,
AlgEquiv.toAlgHom_toRingHom, RingHom.coe_comp, AlgEquiv.coe_trans,
Function.comp_apply, MvPolynomial.sumAlgEquiv_symm_apply, iterToSum_C_C,
renameEquiv_apply, Equiv.coe_trans, Equiv.sumComm_apply]
· intro
simp only [eqv, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, rename_X,
AlgEquiv.toAlgHom_toRingHom, RingHom.coe_comp, AlgEquiv.coe_trans,
Function.comp_apply, MvPolynomial.sumAlgEquiv_symm_apply, iterToSum_C_X,
renameEquiv_apply, Equiv.coe_trans, Equiv.sumComm_apply, Sum.swap_inr,
Equiv.Set.sumCompl_apply_inl]
· simp [eqv]
· simp [eqv]
apply_fun (· p) at this
simp only [AlgHom.toRingHom_eq_coe, RingHom.coe_coe, AlgEquiv.toAlgHom_toRingHom,
RingHom.coe_comp, Function.comp_apply] at this
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