def red_fin_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/reducek.bend:84

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/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/reduce.bend as R

84def red_fin_v(+one: Nat, +h1: {one == 1n : Nat}, +mp: Nat, +c: List<&2, Nat>, +hm: {Nat.add(1n+mp, LV.ev(c)) == C.shift(256n, one) : Nat}, +hcc: {Nat.is_lt(Nat.add(LV.ev(c), LV.ev(c)), C.shift(256n, one)) == True{} : Bool}, +r: List<&2, Nat>, +hlo: {FS.limbs16(one, 16n, L.take(16n, r)) == True{} : Bool}, +hr: {Nat.is_lt(LV.ev(r), C.shift(256n, one)) == True{} : Bool}) -> {LV.ev(L.canon(c, L.take(16n, r))) == Nat.mod(LV.ev(r), 1n+mp) : Nat}:
85  +et = R.take_small(one, h1, r, hr)
86  +hv = I.lt_subst_l(LV.ev(r), LV.ev(L.take(16n, r)), C.shift(256n, one), Equal.sym(Nat, LV.ev(L.take(16n, r)), LV.ev(r), et), hr)
87  %Equal.sym(Nat, LV.ev(L.canon(c, L.take(16n, r))), Nat.mod(LV.ev(L.take(16n, r)), 1n+mp), R.canon_v(one, h1, mp, c, L.take(16n, r), hlo, hv, hm, hcc)) : {_ == Nat.mod(LV.ev(r), 1n+mp) : Nat}
88  %Equal.sym(Nat, LV.ev(L.take(16n, r)), LV.ev(r), et) : {Nat.mod(_, 1n+mp) == Nat.mod(LV.ev(r), 1n+mp) : Nat}
89  {==}