F64tools.dz: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64tools.bend as F64tools
Lines 36-41 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64tools.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64tools.bend&start_line=36&end_line=41

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/f64.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64cmp.bend as FC

def dz(+E: Nat, +z: Bool) -> {F.dexp_z(E, z) == SF.pick(Nat, z, Nat.sub(SF.zb(), 1074n), Nat.sub(Nat.add(E, SF.zb()), 1075n)) : Nat}:
  match z:
    case True{}:
      {==}
    case False{}:
      Equal.sym(Nat, Nat.sub(Nat.add(E, SF.zb()), 1075n), Nat.add(E, 1925n), Equal.trans(Nat, Nat.sub(Nat.add(E, SF.zb()), 1075n), Nat.add(1925n, E), Nat.add(E, 1925n), FC.esub(E), NA.add_comm(1925n, E)))

Uses (11):
  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.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64cmp.bend&name=esub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=pick
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=zb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=dexp_z