F64divv.dbl53: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divv.bend as F64divv
Lines 78-80 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divv.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divv.bend&start_line=78&end_line=80

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/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

# 2^53 <= 2 n and n < 2 m for normalized n, m
def dbl53(+one: Nat, +h1: {one == 1n : Nat}, +n: Nat, +h: {C.fits(52n, n) == False{} : Bool}) -> {Nat.is_le(C.shift(53n, one), Nat.add(n, n)) == True{} : Bool}:
  L.subst(Nat, z => {Nat.is_le(C.shift(53n, one), z) == True{} : Bool}, Nat.double(n), Nat.add(n, n), NA.double_self(n), N.double_le(C.shift(52n, one), n, lo52(one, h1, n, h)))

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=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=Base/base.bend&name=Nat.is_le
  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/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=double_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divv.bend&name=lo52
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift