def one_e
bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/scalarpow.bend:95
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarpow.bend as Scalarpow
import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend as S
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as K
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/modexp.bend as ME
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend as SO
95def one_e(+one: Nat, +h1: {one == 1n : Nat}, +x: Nat) -> {LV.ev(S.one()) == Nat.mod(Nat.pow(x, 0n), 1n+K.np(one)) : Nat}:
96 +ev = Equal.trans(Nat, LV.ev(S.one()), FS.value(one, S.one()), 1n, Equal.sym(Nat, FS.value(one, S.one()), LV.ev(S.one()), LV.ev_value(one, h1, S.one())), SO.small_val(one, h1, 1n, one_lt(one, h1)))
97 Equal.trans(Nat, LV.ev(S.one()), 1n, Nat.mod(Nat.pow(x, 0n), 1n+K.np(one)), ev, ME.pow0(K.np(one), x, I.lt_subst_r(1n, FS.order(one), 1n+K.np(one), K.order_eq(one, h1), one_lt(one, h1))))