Canon.and1: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend as Canon
Lines 176-182 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&start_line=176&end_line=182

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
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/math/natural/arith.bend as NR
import bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend as PD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M

def and1(+one: Nat, +h1: {one == 1n : Nat}, +l: U32) -> {v(U32.and(l, 1)) == Nat.mod(v(l), 2n) : Nat}:
  +a = PD.and32(1n, l, 1, {==})
  +b = PD.and32_lt(1n, one, h1, l, 1, {==})
  +hp = PD.hp32(1n, l)
  +b2 = L.subst(Nat, o => {Nat.is_lt(v(U32.and(l, 1)), WD.sc(1n, o)) == True{} : Bool}, one, 1n, h1, b)
  +e1 = Equal.trans(Nat, v(l), Nat.add(v(U32.and(l, 1)), WD.sc(1n, hp)), Nat.add(Nat.mul(hp, 2n), v(U32.and(l, 1))), a, Equal.trans(Nat, Nat.add(v(U32.and(l, 1)), WD.sc(1n, hp)), Nat.add(WD.sc(1n, hp), v(U32.and(l, 1))), Nat.add(Nat.mul(hp, 2n), v(U32.and(l, 1))), NA.add_comm(v(U32.and(l, 1)), WD.sc(1n, hp)), M.cong_l(WD.sc(1n, hp), Nat.mul(hp, 2n), v(U32.and(l, 1)), Equal.trans(Nat, Nat.double(hp), Nat.mul(2n, hp), Nat.mul(hp, 2n), NA.double_mul(hp), NA.mul_comm(2n, hp)))))
  Equal.sym(Nat, Nat.mod(v(l), 2n), v(U32.and(l, 1)), Equal.trans(Nat, Nat.mod(v(l), 2n), Nat.mod(Nat.add(Nat.mul(hp, 2n), v(U32.and(l, 1))), 2n), v(U32.and(l, 1)), M.cong_mod(2n, v(l), Nat.add(Nat.mul(hp, 2n), v(U32.and(l, 1))), e1), NR.mod_of(hp, 1n, v(U32.and(l, 1)), b2)))

Uses (23):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=cong_l
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=cong_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=double_mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&name=mod_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend&name=and32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend&name=and32_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend&name=hp32