W64sqrt.le16: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend as W64sqrt
Lines 251-252 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend&start_line=251&end_line=252

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/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

def le16(+one: Nat, +h1: {one == 1n : Nat}, +r: U32, +m: U32, +pm: {m == U32{WD.mask(32n, 16n)} : U32}, +h: {Nat.is_lt(v(r), WD.sc(16n, one)) == True{} : Bool}) -> {Nat.is_le(v(r), v(m)) == True{} : Bool}:
  N.lt_succ_le(v(r), v(m), L.subst(Nat, z => {Nat.is_lt(v(r), z) == True{} : Bool}, WD.sc(16n, one), 1n+v(m), Equal.sym(Nat, 1n+v(m), WD.sc(16n, one), m16(one, h1, m, pm)), h))

Uses (12):
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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_succ_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=mask
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend&name=m16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend&name=v