F64sqk.four: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqk.bend as F64sqk
Lines 40-41 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqk.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqk.bend&start_line=40&end_line=41

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

def four(+x: Nat) -> {C.shift(2n, x) == Nat.add(Nat.add(x, x), Nat.add(x, x)) : Nat}:
  Equal.trans(Nat, Nat.double(Nat.double(x)), Nat.add(Nat.double(x), Nat.double(x)), Nat.add(Nat.add(x, x), Nat.add(x, x)), NA.double_self(Nat.double(x)), Equal.trans(Nat, Nat.add(Nat.double(x), Nat.double(x)), Nat.add(Nat.add(x, x), Nat.double(x)), Nat.add(Nat.add(x, x), Nat.add(x, x)), Equal.cong(Nat, Nat, z => Nat.add(z, Nat.double(x)), Nat.double(x), Nat.add(x, x), NA.double_self(x)), Equal.cong(Nat, Nat, z => Nat.add(Nat.add(x, x), z), Nat.double(x), Nat.add(x, x), NA.double_self(x))))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=double_self
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift