def dz

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64tools.bend:36

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

36def 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}:
37  match z:
38    case True{}:
39      {==}
40    case False{}:
41      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)))