Lemma isapropisafield (X : commring) : isaprop (isafield X). Proof. use isofhleveltotal2. - apply propproperty. - intros H. use impred. intros x. use isapropcoprod. + use isapropinvpair. + use setproperty. + intros H' e. use H. refine (_ @ multx0_is_l _ (ringop2axs X) (ringdistraxs X) (pr1 H')). refine (_ @ maponpaths _ e). exact (!dirprod_pr1 (pr2 H')). Qed.
Require Import UniMath.Algebra.Groups.