Listops.eq_digit_f: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend as Listops
Lines 120-124 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend&start_line=120&end_line=124

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/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as Lg

def eq_digit_f(+one: Nat, +h1: {one == 1n : Nat}, +x: Nat, +y: Nat, +a: Nat, +b: Nat, +hx: {Nat.is_lt(x, C.shift(16n, one)) == True{} : Bool}, +hy: {Nat.is_lt(y, C.shift(16n, one)) == True{} : Bool}, +h: {Nat.is_eq(Nat.add(x, C.shift(16n, a)), Nat.add(y, C.shift(16n, b))) == True{} : Bool}) -> {Bool.and(Nat.is_eq(x, y), Nat.is_eq(a, b)) == True{} : Bool}:
  +e = N.eq_from_is_eq(Nat.add(x, C.shift(16n, a)), Nat.add(y, C.shift(16n, b)), h)
  +exy = uniq_lo(one, h1, x, y, a, b, hx, hy, e)
  +eab = uniq_hi(one, h1, x, y, a, b, hx, hy, e)
  Lg.and_intro(Nat.is_eq(x, y), Nat.is_eq(a, b), Lg.subst(Nat, z => {Nat.is_eq(x, z) == True{} : Bool}, x, y, exy, N.is_eq_refl(x)), Lg.subst(Nat, z => {Nat.is_eq(a, z) == True{} : Bool}, a, b, eab, N.is_eq_refl(a)))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend&name=uniq_hi
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend&name=uniq_lo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  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/nat.bend&name=eq_from_is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=is_eq_refl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift