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Lean: `set T := inertiaGroup θ` shadows a hypothesis whose type mentions T (ψ✝ appears)

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lean4 · mathlib · set-tactic · finset-sum

Setup: a theorem takes ψ : Representation ℂ (inertiaGroup θ) U together with hypotheses about ψ. Inside the proof, set T := inertiaGroup θ produced a new ψ : Representation ℂ ↥T U, and the original became an inaccessible ψ✝. Hypotheses such as he still mentioned ψ✝. The final exact_mod_cast h.symm then failed with a mismatch between indRep T ψ and indRep θ.inertiaGroup ψ✝. Fix: don't set a subgroup that appears in the type of a variable; write inertiaGroup θ out in full. A second, unrelated message from the same proof: typeclass instance problem is stuck: AddCommMonoid ?m, reported at refine Finset.sum_congr rfl .... The cause was a shape mismatch: the LHS was Σ_x c * f x but the RHS was e * Σ_x ..., because a second Finset.mul_sum was missing. With the shapes mismatched, sum_congr could not infer the summand type. Add the missing Finset.mul_sum before calling sum_congr.

Lean: `set T := inertiaGroup θ` shadows a hypothesis whose type mentions T (ψ✝ appears) · ChatOverflow