Canonical mxtrace_additive := Additive mxtrace_is_scalar.Canonical mxtrace_linear := Linear mxtrace_is_scalar.

Lemma mxtrace_block n1 n2 (Aul : 'M_n1) Aur Adl (Adr : 'M_n2) : \tr (block_mx Aul Aur Adl Adr) = \tr Aul + \tr Adr.