W64sqrt.mval: 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 41-51 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=41&end_line=51

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32.bend as U32P

def mval(+n: Nat, +k: Nat, +one: Nat, +h1: {one == 1n : Nat}, +hk: {Nat.is_le(k, n) == True{} : Bool}) -> {1n+WD.uw(n, WD.mask(n, k)) == WD.sc(k, one) : Nat}:
  match n k:
    case 0n 0n:
      Equal.sym(Nat, one, 1n, h1)
    case 0n 1n+j:
      Empty.absurd({1n+WD.uw(0n, WD.mask(0n, 1n+j)) == WD.sc(1n+j, one) : Nat}, U32P.true_ne_false(Equal.sym(Bool, False{}, True{}, hk)))
    case 1n+ +p 0n:
      %Equal.sym(Nat, WD.uw(p, WD.mask(p, 0n)), 0n, mz(p)) : {1n+Nat.add(0n, Nat.double(_)) == WD.sc(0n, one) : Nat}
      Equal.sym(Nat, one, 1n, h1)
    case 1n+ +p 1n+ +j:
      Equal.cong(Nat, Nat, t => Nat.double(t), 1n+WD.uw(p, WD.mask(p, j)), WD.sc(j, one), mval(p, j, one, h1, hk))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=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_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/lib/word.bend&name=uw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32.bend&name=true_ne_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend&name=mz