proposition: Lemma expn_snum_subproof (xnz nnz : nullity) (xr nr : reality) (x : {compare 0 & xnz & xr}) (n : {compare 0 & 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. move: xr nr xnz nnz x n => [[[]|]|] [[[]|]|] [] []// x n; do ?[by case: (bottom x)|by case: (bottom n) |by rewrite ?eq0 ?expn0// expn_eq0 ?eq0F]. move: xr nr xnz nnz x n => [[[]|]|] [[[]|]|] [] []/= x [[|n]//= _] //; do ?[by case: (bottom x)|by case: (bottom n)|by rewrite eq0 exp0n]. Qed.
imports: HB(structures) Coq(ssreflect ssrfun ssrbool) mathcomp(ssrnat eqtype choice order ssralg ssrnum ssrint) mathcomp(mathcomp_extra)