Fround.sub_add_r: 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 65-67 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=65&end_line=67

import Base
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/lemmas/proofs/nat_algebra.bend as NA

def sub_add_r(+a: Nat, +b: Nat, +m: Nat, +h: {Nat.is_le(m, a) == True{} : Bool}) -> {Nat.sub(Nat.add(a, b), m) == Nat.add(Nat.sub(a, m), b) : Nat}:
  +d = Nat.sub(a, m)
  Equal.trans(Nat, Nat.sub(Nat.add(a, b), m), Nat.sub(Nat.add(Nat.add(m, d), b), m), Nat.add(d, b), Equal.cong(Nat, Nat, z => Nat.sub(Nat.add(z, b), m), a, Nat.add(m, d), Equal.sym(Nat, Nat.add(m, d), a, N.sub_add(a, m, h))), Equal.trans(Nat, Nat.sub(Nat.add(Nat.add(m, d), b), m), Nat.sub(Nat.add(m, Nat.add(d, b)), m), Nat.add(d, b), Equal.cong(Nat, Nat, z => Nat.sub(z, m), Nat.add(Nat.add(m, d), b), Nat.add(m, Nat.add(d, b)), NA.add_assoc(m, d, b)), N.add_sub_cancel(m, Nat.add(d, b))))

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.cong
  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.is_le
  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_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_sub_cancel
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_add