def lt_p_red

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/paff.bend:73

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/field.bend as F
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/fwrap.bend as FW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT

73def lt_p_red(+one: Nat, +h1: {one == 1n : Nat}, +x: List<&2, Nat>, +hl: {FS.limbs16(one, 16n, x) == True{} : Bool}, +h: {F.lt_p(x) == True{} : Bool}) -> {PT.red(one, x) == True{} : Bool}:
74  +hv = Equal.trans(Bool, Nat.is_lt(FS.value(one, x), FS.prime(one)), F.lt_p(x), True{}, Equal.sym(Bool, F.lt_p(x), Nat.is_lt(FS.value(one, x), FS.prime(one)), FW.lt_p_f(one, h1, x)), h)
75  Lg.and_intro(FS.limbs16(one, 16n, x), Nat.is_lt(FS.value(one, x), FS.prime(one)), hl, hv)