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

(* Specifications: *)
Lemma mxtrace0 : \tr 0 = 0.
Lemma mxtraceD A B : \tr (A + B) = \tr A + \tr B.
Lemma trace_mx11 (A : 'M_1) : \tr A = A 0 0.
Lemma mxtrace_block n1 n2 (Aul : 'M_n1) Aur Adl (Adr : 'M_n2) : \tr (block_mx Aul Aur Adl Adr) = \tr Aul + \tr Adr.