def reduce4_vv

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/reducek.bend:142

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/lib/logic.bend as Lg
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV

142def reduce4_vv(+one: Nat, +h1: {one == 1n : Nat}, +mp: Nat, +c: List<&2, Nat>, +hm: {Nat.add(1n+mp, FS.value(one, c)) == C.shift(256n, one) : Nat}, +hcc: {Nat.is_lt(Nat.add(FS.value(one, c), FS.value(one, c)), C.shift(256n, one)) == True{} : Bool}, +hb1: {Nat.is_le(Nat.mul(1n+FS.value(one, c), FS.value(one, c)), Nat.mul(4n, C.shift(256n, one))) == True{} : Bool}, +hb2: {Nat.is_le(Nat.add(Nat.mul(5n, FS.value(one, c)), FS.value(one, c)), C.shift(256n, one)) == True{} : Bool}, +xs: List<&2, Nat>, +hx: {Nat.is_lt(LV.ev(xs), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}) -> {LV.ev(L.reduce(c, 4n, xs)) == Nat.mod(LV.ev(xs), 1n+mp) : Nat}:
143  +e = hv_ev(one, h1, c)
144  +hm2 = Lg.subst(Nat, z => {Nat.add(1n+mp, z) == C.shift(256n, one) : Nat}, FS.value(one, c), LV.ev(c), e, hm)
145  +hcc2 = Lg.subst(Nat, z => {Nat.is_lt(Nat.add(z, z), C.shift(256n, one)) == True{} : Bool}, FS.value(one, c), LV.ev(c), e, hcc)
146  +hb12 = Lg.subst(Nat, z => {Nat.is_le(Nat.mul(1n+z, z), Nat.mul(4n, C.shift(256n, one))) == True{} : Bool}, FS.value(one, c), LV.ev(c), e, hb1)
147  +hb22 = Lg.subst(Nat, z => {Nat.is_le(Nat.add(Nat.mul(5n, z), z), C.shift(256n, one)) == True{} : Bool}, FS.value(one, c), LV.ev(c), e, hb2)
148  reduce4_v(one, h1, mp, c, hm2, hcc2, hb12, hb22, xs, hx)