Section GL_unit.
Variables (n : nat) (R : finComUnitRingType).
Canonical GL_subType := [subType of {'GL_n[R]} for GLval].
Definition GL_eqMixin := Eval hnf in [eqMixin of {'GL_n[R]} by <:].
Canonical GL_eqType := Eval hnf in EqType {'GL_n[R]} GL_eqMixin.
Canonical GL_choiceType := Eval hnf in [choiceType of {'GL_n[R]}].
Canonical GL_countType := Eval hnf in [countType of {'GL_n[R]}].
Canonical GL_subCountType := Eval hnf in [subCountType of {'GL_n[R]}].
Canonical GL_finType := Eval hnf in [finType of {'GL_n[R]}].
Canonical GL_subFinType := Eval hnf in [subFinType of {'GL_n[R]}].
Canonical GL_baseFinGroupType := Eval hnf in [baseFinGroupType of {'GL_n[R]}].
Canonical GL_finGroupType := Eval hnf in [finGroupType of {'GL_n[R]}].
Definition GLgroup of phant R := [set: {'GL_n[R]}].
Canonical GLgroup_group ph := Eval hnf in [group of GLgroup ph].
Implicit Types u v : {'GL_n[R]}.

Lemma GL_det u : \det u != 0.