Fround.fits_add1: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/fround.bend as Fround
Lines 57-63 of bend-collections-laws-math@1.0.0.0/proofs/math/random/fround.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/fround.bend&start_line=57&end_line=63

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
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW

def fits_add1(+k: Nat, +a: Nat, +b: Nat, +ha: {C.fits(k, a) == True{} : Bool}, +hb: {C.fits(k, b) == True{} : Bool}) -> {C.fits(1n+k, Nat.add(a, b)) == True{} : Bool}:
  +P = C.pow2(k)
  +h1 = N.lt_add_r2(a, P, b, WW.lt_of_fits(k, a, ha))
  +h2 = N.lt_add_left(b, P, P, WW.lt_of_fits(k, b, hb))
  +h3 = N.lt_trans(Nat.add(a, b), Nat.add(P, b), Nat.add(P, P), h1, h2)
  +h4 = L.subst(Nat, z => {Nat.is_lt(Nat.add(a, b), z) == True{} : Bool}, Nat.add(P, P), Nat.double(P), Equal.sym(Nat, Nat.double(P), Nat.add(P, P), NA.double_self(P)), h3)
  WW.fits_of_lt(1n+k, Nat.add(a, b), h4)

Uses (15):
  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=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_lt
  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=lt_add_left
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_add_r2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend&name=fits_of_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend&name=lt_of_fits
  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=pow2