Float.lt_c: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend as Float
Lines 451-456 of bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&start_line=451&end_line=456

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F

def lt_c(+vm: Nat, +x: WU.U64, +hv: {SW.value(mm(x)) == vm : Nat}) -> {F.lt(R.to_float(x), F.one()) == True{} : Bool}:
  match vm:
    case 0n:
      lt_z_case(x, hv)
    case 1n+np:
      lt_s_case(x, np, hv)

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=lt_s_case
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=lt_z_case
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=mm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/w64.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=to_float
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64