@@ -130,7 +130,7 @@ lemma lemma2 [Module A G] (S : systemOfUnits p G s) (hs : S.IsFundamental)
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let a' := a.comapDomain (Fin.succAbove i) Fin.succAbove_right_injective.injOn
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have hS' : S'.units ∘ Fin.succAbove i = S.units ∘ Fin.succAbove i := by
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ext; simp only [Function.comp_apply, ne_eq, Fin.succAbove_ne, not_false_eq_true,
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- Function.update_noteq ]
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+ Function.update_of_ne ]
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have ha' :
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Finsupp.linearCombination A (S'.units ∘ Fin.succAbove i) a' + S.units i = (1 - zeta p) • g := by
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rw [hS', Finsupp.linearCombination_comp, LinearMap.comp_apply, Finsupp.lmapDomain_apply,
@@ -158,11 +158,11 @@ lemma lemma2 [Module A G] (S : systemOfUnits p G s) (hs : S.IsFundamental)
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· rw [add_comm, ← eq_sub_iff_add_eq] at ha'
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rw [← hij, ha']
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apply sub_mem
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- · exact Submodule.smul_mem _ _ (Submodule.subset_span ⟨i, Function.update_same _ _ _⟩)
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+ · exact Submodule.smul_mem _ _ (Submodule.subset_span ⟨i, Function.update_self _ _ _⟩)
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· rw [← Finsupp.range_linearCombination, Finsupp.linearCombination_comp, LinearMap.comp_apply]
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exact ⟨_, rfl⟩
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- · exact Submodule.subset_span ⟨j, Function.update_noteq (Ne.symm hij) _ _⟩
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- · refine ⟨g, Submodule.subset_span ⟨i, Function.update_same _ _ _⟩, ?_⟩
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+ · exact Submodule.subset_span ⟨j, Function.update_of_ne (Ne.symm hij) _ _⟩
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+ · refine ⟨g, Submodule.subset_span ⟨i, Function.update_self _ _ _⟩, ?_⟩
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rw [← Finsupp.range_linearCombination]
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rintro ⟨l, rfl⟩
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letI := (Algebra.id A).toModule
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