def hm_n

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:230

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/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend as SR

230def hm_n(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.add(1n+np(one), FS.cn(one)) == C.shift(256n, one) : Nat}:
231  %Equal.sym(Nat, C.shift(256n, one), Nat.add(Nat.add(FS.cn(one), 1n), np(one)), Equal.sym(Nat, Nat.add(Nat.add(FS.cn(one), 1n), np(one)), C.shift(256n, one), np_sum(one, h1))) : {Nat.add(1n+np(one), FS.cn(one)) == _ : Nat}
232  %Equal.sym(Nat, 1n+np(one), Nat.add(np(one), 1n), SR.succ_add(1n, np(one))) : {Nat.add(_, FS.cn(one)) == Nat.add(Nat.add(FS.cn(one), 1n), np(one)) : Nat}
233  %Equal.sym(Nat, Nat.add(Nat.add(np(one), 1n), FS.cn(one)), Nat.add(np(one), Nat.add(1n, FS.cn(one))), NA.add_assoc(np(one), 1n, FS.cn(one))) : {_ == Nat.add(Nat.add(FS.cn(one), 1n), np(one)) : Nat}
234  %Equal.sym(Nat, Nat.add(1n, FS.cn(one)), Nat.add(FS.cn(one), 1n), NA.add_comm(1n, FS.cn(one))) : {Nat.add(np(one), _) == Nat.add(Nat.add(FS.cn(one), 1n), np(one)) : Nat}
235  %Equal.sym(Nat, Nat.add(np(one), Nat.add(FS.cn(one), 1n)), Nat.add(FS.cn(one), Nat.add(np(one), 1n)), NA.add_swap(np(one), FS.cn(one), 1n)) : {_ == Nat.add(Nat.add(FS.cn(one), 1n), np(one)) : Nat}
236  %Equal.sym(Nat, Nat.add(Nat.add(FS.cn(one), 1n), np(one)), Nat.add(FS.cn(one), Nat.add(1n, np(one))), NA.add_assoc(FS.cn(one), 1n, np(one))) : {Nat.add(FS.cn(one), Nat.add(np(one), 1n)) == _ : Nat}
237  %Equal.sym(Nat, Nat.add(1n, np(one)), Nat.add(np(one), 1n), NA.add_comm(1n, np(one))) : {Nat.add(FS.cn(one), Nat.add(np(one), 1n)) == Nat.add(FS.cn(one), _) : Nat}
238  {==}