def cp_le

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:69

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/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I

69def cp_le(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(FS.cp(one), C.shift(33n, one)) == True{} : Bool}:
70  %Equal.sym(Nat, FS.cp(one), Nat.add(C.shift(32n, one), 977n), cp_eq(one, h1)) : {Nat.is_le(_, C.shift(33n, one)) == True{} : Bool}
71  %Equal.sym(Nat, C.shift(33n, one), Nat.add(C.shift(32n, one), C.shift(32n, one)), Equal.sym(Nat, Nat.add(C.shift(32n, one), C.shift(32n, one)), C.shift(33n, one), shift_twice(32n, one))) : {Nat.is_le(Nat.add(C.shift(32n, one), 977n), _) == True{} : Bool}
72  I.le_add2(C.shift(32n, one), 977n, C.shift(32n, one), C.shift(32n, one), N.le_refl(C.shift(32n, one)), small_le(one, h1, 32n, 977n, {==}))