def hm_p

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/consts.bend:113

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

113def hm_p(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.add(1n+pp(one), FS.cp(one)) == C.shift(256n, one) : Nat}:
114  %Equal.sym(Nat, C.shift(256n, one), Nat.add(Nat.add(FS.cp(one), 1n), pp(one)), Equal.sym(Nat, Nat.add(Nat.add(FS.cp(one), 1n), pp(one)), C.shift(256n, one), pp_sum(one, h1))) : {Nat.add(1n+pp(one), FS.cp(one)) == _ : Nat}
115  %Equal.sym(Nat, 1n+pp(one), Nat.add(pp(one), 1n), SR.succ_add(1n, pp(one))) : {Nat.add(_, FS.cp(one)) == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
116  %Equal.sym(Nat, Nat.add(Nat.add(pp(one), 1n), FS.cp(one)), Nat.add(pp(one), Nat.add(1n, FS.cp(one))), NA.add_assoc(pp(one), 1n, FS.cp(one))) : {_ == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
117  %Equal.sym(Nat, Nat.add(1n, FS.cp(one)), Nat.add(FS.cp(one), 1n), NA.add_comm(1n, FS.cp(one))) : {Nat.add(pp(one), _) == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
118  %Equal.sym(Nat, Nat.add(pp(one), Nat.add(FS.cp(one), 1n)), Nat.add(FS.cp(one), Nat.add(pp(one), 1n)), NA.add_swap(pp(one), FS.cp(one), 1n)) : {_ == Nat.add(Nat.add(FS.cp(one), 1n), pp(one)) : Nat}
119  %Equal.sym(Nat, Nat.add(Nat.add(FS.cp(one), 1n), pp(one)), Nat.add(FS.cp(one), Nat.add(1n, pp(one))), NA.add_assoc(FS.cp(one), 1n, pp(one))) : {Nat.add(FS.cp(one), Nat.add(pp(one), 1n)) == _ : Nat}
120  %Equal.sym(Nat, Nat.add(1n, pp(one)), Nat.add(pp(one), 1n), NA.add_comm(1n, pp(one))) : {Nat.add(FS.cp(one), Nat.add(pp(one), 1n)) == Nat.add(FS.cp(one), _) : Nat}
121  {==}