Float.value_s: 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 348-354 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=348&end_line=354

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/spec/math/f64.bend as SF
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/w64.bend as X
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
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW

def value_s(+x: WU.U64, +n: Nat, +hn: {C.low(53n, SW.value(x)) == n : Nat}, +np: Nat, +xv: Nat, +hx: {Nat.sub(SF.zb(), 53n) == xv : Nat}, +hv: {SW.value(mm(x)) == 1n+np : Nat}) -> {R.to_float(x) == SF.round(False{}, n, xv) : F.F64}:
  +hl = hl_of(x, 1n+np, hv)
  +h1 = Equal.trans(Nat, n, C.low(53n, SW.value(x)), 1n+np, Equal.sym(Nat, C.low(53n, SW.value(x)), n, hn), hl)
  +hf = Equal.trans(Bool, C.fits(53n, 1n+np), C.fits(53n, C.low(53n, SW.value(x))), True{}, Equal.cong(Nat, Bool, z => C.fits(53n, z), 1n+np, C.low(53n, SW.value(x)), Equal.sym(Nat, C.low(53n, SW.value(x)), 1n+np, hl)), WW.low_fits(53n, SW.value(x)))
  %Equal.sym(Nat, n, 1n+np, h1) : {R.to_float(x) == SF.round(False{}, _, xv) : F.F64}
  %Equal.sym(Bool, X.is_zero(mm(x)), Nat.is_eq(1n+np, 0n), iz(mm(x), 1n+np, hv)) : {R.f53_z(mm(x), _) == SF.round(False{}, 1n+np, xv) : F.F64}
  Equal.trans(F.F64, R.f53_z(mm(x), Nat.is_eq(1n+np, 0n)), R.f53(mm(x), X.clz(mm(x))), SF.round(False{}, 1n+np, xv), {==}, main_v(1n, {==}, xv, hx, mm(x), np, hv, hf))

Uses (24):
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=hl_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=iz
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=main_v
  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/proofs/math/typed/width.bend&name=low_fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=low
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=round
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=zb
  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=F64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=f53
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=f53_z
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=clz
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=is_zero