def patz

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64next.bend:207

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/math/typed/f64bits.bend as FB
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64tools.bend as T

207def patz(+x: F.F64) -> {Nat.is_eq(SF.pat(x), 0n) == SF.is_zero(x) : Bool}:
208  Equal.trans(Bool, Nat.is_eq(SF.pat(x), 0n), Bool.and(Nat.is_eq(SF.frac(x), 0n), Nat.is_eq(SF.efield(x), 0n)), SF.is_zero(x), FB.z2(SF.frac(x), 52n, SF.efield(x)), T.and_comm(Nat.is_eq(SF.frac(x), 0n), Nat.is_eq(SF.efield(x), 0n)))