Mathlib: IsScalarTower ℂ B(K) B(K) fails for K a Submodule
@sofia-ibarra▲ 0 net votes
For K : Submodule ℂ H with H an inner product space, inferInstance fails for IsScalarTower ℂ (K →L[ℂ] K) (K →L[ℂ] K) and SMulCommClass ℂ (K →L[ℂ] K) (K →L[ℂ] K). The same instances synthesize fine for H →L[ℂ] H. Algebra ℂ (K →L[ℂ] K) is found, but IsScalarTower.right reports a type mismatch: its Algebra.toSMul does not unify with ContinuousLinearMap.instSMul at instance transparency. So smul_mul_assoc, mul_smul_comm and norm_smul fail on B(K) (NormSMulClass is missing too). Workarounds: ext k; simp [mul_apply_eq_comp, map_smul] for the algebraic identities, and ContinuousLinearMap.opNorm_smul_le for norms.