PROOFText.wsd.mle: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_text.bend as PROOFText
Lines 121-123 of bend-osdev-word64@0.1.1.0/PROOF_text.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&start_line=121&end_line=123

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# a c < b c: a < b
def wsd.mle(+x: Nat, +y: Nat, +c: Nat, +h: {Nat.is_le(x, y) == True{} : Bool}) -> {Nat.is_le(Nat.mul(x, c), Nat.mul(y, c)) == True{} : Bool}:
  Equal.trans(Bool, Nat.is_le(Nat.mul(x, c), Nat.mul(y, c)), Nat.is_le(Nat.mul(x, c), Nat.add(Nat.mul(Nat.sub(y, x), c), Nat.mul(x, c))), True{}, Equal.sym(Bool, Nat.is_le(Nat.mul(x, c), Nat.add(Nat.mul(Nat.sub(y, x), c), Nat.mul(x, c))), Nat.is_le(Nat.mul(x, c), Nat.mul(y, c)), Equal.cong(Nat, Bool, zz => Nat.is_le(Nat.mul(x, c), zz), Nat.add(Nat.mul(Nat.sub(y, x), c), Nat.mul(x, c)), Nat.mul(y, c), Equal.trans(Nat, Nat.add(Nat.mul(Nat.sub(y, x), c), Nat.mul(x, c)), Nat.mul(Nat.add(Nat.sub(y, x), x), c), Nat.mul(y, c), wr.t1(Nat.sub(y, x), c, x), Equal.cong(Nat, Nat, zz => Nat.mul(zz, c), Nat.add(Nat.sub(y, x), x), y, UL.nat_le_witness(x, y, h))))), UL.nat_le_add(Nat.mul(x, c), Nat.mul(Nat.sub(y, x), c)))

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.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.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_le_add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_le_witness
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&name=wr.t1