proposition: Lemma exprn_snum_subproof (xnz nnz : nullity) (xr nr : reality) (x : {num R & xnz & xr}) (n : {compare 0%N & nnz & nr}) (rnz := exprn_nonzero_subdef xnz nnz xr nr) (rrl := exprn_reality_subdef xnz nnz xr nr) : Signed.spec 0 rnz rrl (x%:num ^+ n%:num).
proof: Proof. rewrite {}/rnz {}/rrl; apply/andP; split. by move: xr nr xnz nnz x n => [[[]|]|] [[[]|]|] [] []// x n; do ?[by case: (bottom x)|by case: (bottom n)]; rewrite expf_eq0/= ?eq0// ?eq0F ?andbF//. move: xr nr xnz nnz x n => [[[]|]|] [[[]|]|] [] []/= x [[|n]//= _] //; do ?[by case: (bottom x)|by case: (bottom n)|by rewrite [_ || _]realX |by rewrite eq0 expr0n|exact: exprn_ge0|by rewrite expr0 ler01]. Qed.
imports: HB(structures) Coq(ssreflect ssrfun ssrbool) mathcomp(ssrnat eqtype choice order ssralg ssrnum ssrint) mathcomp(mathcomp_extra)