def neg_v
bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fieldops.bend:164
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend as Fieldops
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/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend as F
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/fprot.bend as FR
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/negate.bend as NG
164def neg_v(+one: Nat, +h1: {one == 1n : Nat}, +b: List<&2, Nat>, +hb: {FS.reduced(one, FS.prime(one), b) == True{} : Bool}) -> {FS.value(one, F.neg(b)) == FS.mneg(FS.prime(one), FS.value(one, b)) : Nat}:
165 %Equal.sym(List<&2, Nat>, F.neg(b), F.neg_u(b), FR.f_neg(b)) : {FS.value(one, _) == FS.mneg(FS.prime(one), FS.value(one, b)) : Nat}
166 %Equal.sym(Nat, FS.value(one, F.reduce(L.neg_raw(F.c(), b))), Nat.mod(LV.ev(L.neg_raw(F.c(), b)), FS.prime(one)), red_v(one, h1, L.neg_raw(F.c(), b), neg_hx(one, h1, b, hb))) : {_ == Nat.mod(Nat.sub(Nat.add(0n, FS.prime(one)), Nat.mod(FS.value(one, b), FS.prime(one))), FS.prime(one)) : Nat}
167 %Equal.sym(Nat, FS.value(one, b), LV.ev(b), LV.ev_value(one, h1, b)) : {Nat.mod(LV.ev(L.neg_raw(F.c(), b)), FS.prime(one)) == Nat.mod(Nat.sub(Nat.add(0n, FS.prime(one)), Nat.mod(_, FS.prime(one))), FS.prime(one)) : Nat}
168 %Equal.sym(Nat, FS.prime(one), 1n+K.pp(one), K.prime_eq(one, h1)) : {Nat.mod(LV.ev(L.neg_raw(F.c(), b)), _) == Nat.mod(Nat.sub(Nat.add(0n, FS.prime(one)), Nat.mod(LV.ev(b), FS.prime(one))), FS.prime(one)) : Nat}
169 %Equal.sym(Nat, FS.prime(one), 1n+K.pp(one), K.prime_eq(one, h1)) : {Nat.mod(LV.ev(L.neg_raw(F.c(), b)), 1n+K.pp(one)) == Nat.mod(Nat.sub(Nat.add(0n, _), Nat.mod(LV.ev(b), FS.prime(one))), FS.prime(one)) : Nat}
170 %Equal.sym(Nat, FS.prime(one), 1n+K.pp(one), K.prime_eq(one, h1)) : {Nat.mod(LV.ev(L.neg_raw(F.c(), b)), 1n+K.pp(one)) == Nat.mod(Nat.sub(Nat.add(0n, 1n+K.pp(one)), Nat.mod(LV.ev(b), _)), FS.prime(one)) : Nat}
171 %Equal.sym(Nat, FS.prime(one), 1n+K.pp(one), K.prime_eq(one, h1)) : {Nat.mod(LV.ev(L.neg_raw(F.c(), b)), 1n+K.pp(one)) == Nat.mod(Nat.sub(Nat.add(0n, 1n+K.pp(one)), Nat.mod(LV.ev(b), 1n+K.pp(one))), _) : Nat}
172 NG.sub_mod(K.pp(one), 0n, LV.ev(b), LV.ev(L.neg_raw(F.c(), b)), rlt(one, h1, b, hb), negr_e(one, h1, b, hb))