PROOF.AP.double_le: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 778-781 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=778&end_line=781

import Base

def AP.double_le(+x: Nat, +y: Nat, h: {Nat.is_le(x, y) == True{} : Bool}) -> {Nat.is_le(Nat.double(x), Nat.double(y)) == True{} : Bool}:
  %Equal.sym(Cmp, Nat.cmp(AP.bv(False{}, x), AP.bv(False{}, y)), Word.cmp.fin(False{}, False{}, Nat.cmp(x, y)), AP.nc(x, y, False{}, False{})) : {Cmp.is_le(_) == True{} : Bool}
  %Equal.sym(Bool, Cmp.is_le(Word.cmp.fin(False{}, False{}, Nat.cmp(x, y))), Cmp.is_le(Nat.cmp(x, y)), AP.fin_le_ff(Nat.cmp(x, y))) : {_ == True{} : Bool}
  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=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_le
  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.cmp
  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=Base/base.bend&name=Word.cmp.fin
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.bv
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.fin_le_ff
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.nc