def add_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/scalarops.bend:93

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/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/fprot.bend as FR

93def add_v(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>, +b: List<&2, Nat>, +ha: {FS.reduced(one, FS.order(one), a) == True{} : Bool}, +hb: {FS.reduced(one, FS.order(one), b) == True{} : Bool}) -> {FS.value(one, S.add(a, b)) == FS.madd(FS.order(one), FS.value(one, a), FS.value(one, b)) : Nat}:
94  %Equal.sym(List<&2, Nat>, S.add(a, b), S.add_u(a, b), FR.s_add(a, b)) : {FS.value(one, _) == FS.madd(FS.order(one), FS.value(one, a), FS.value(one, b)) : Nat}
95  %Equal.sym(Nat, FS.value(one, S.reduce_u(L.add(a, b))), Nat.mod(LV.ev(L.add(a, b)), FS.order(one)), red_v(one, h1, L.add(a, b), add_hx(one, h1, a, b, ha, hb))) : {_ == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : Nat}
96  %Equal.sym(Nat, LV.ev(L.add(a, b)), Nat.add(LV.ev(a), LV.ev(b)), LV.add_v(a, b)) : {Nat.mod(_, FS.order(one)) == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : Nat}
97  %Equal.sym(Nat, LV.ev(a), FS.value(one, a), Equal.sym(Nat, FS.value(one, a), LV.ev(a), LV.ev_value(one, h1, a))) : {Nat.mod(Nat.add(_, LV.ev(b)), FS.order(one)) == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : Nat}
98  %Equal.sym(Nat, LV.ev(b), FS.value(one, b), Equal.sym(Nat, FS.value(one, b), LV.ev(b), LV.ev_value(one, h1, b))) : {Nat.mod(Nat.add(FS.value(one, a), _), FS.order(one)) == Nat.mod(Nat.add(FS.value(one, a), FS.value(one, b)), FS.order(one)) : Nat}
99  {==}