proposition: Lemma classicPT (P : Type) : classically P <-> ((P -> False) -> False).
proof: Proof. split; first by move=>/(_ false) PFF PF; suff: false by []; apply: PFF => /PF. by move=> PFF []// Pf; suff: False by []; apply: PFF => /Pf. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra all_solvable) mathcomp(all_field)