F64round.rpfE: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend as F64round
Lines 780-790 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend&start_line=780&end_line=790

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/f64.bend as SF
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/f64.bend as F
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/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA

def rpfE(+s: Bool, +E: Nat, +w: WU.U64, +hS: {C.fits(63n, SW.value(w)) == True{} : Bool}, +hE: {C.fits(11n, E) == True{} : Bool}, +hz: {C.fits(52n, SF.rne(SW.value(w), 10n)) == False{} : Bool}, +hq: {C.fits(63n, Nat.add(SF.rne(SW.value(w), 10n), C.shift(52n, E))) == True{} : Bool}) -> {F.rp_fin(s, E, w) == bits(s, Nat.add(SF.rne(SW.value(w), 10n), C.shift(52n, E))) : F.F64}:
  +r = X.clear0(X.shr(X.add(w, WU.U64{512, 0}), 10n), U32.is_eq(U32.and(X.lo(w), 1023), 512))
  +q = SF.rne(SW.value(w), 10n)
  +ev = rpw(w, hS)
  z0 = WA.is_zero_value(r)
  +hzr = Equal.trans(Bool, X.is_zero(r), Nat.is_eq(SW.value(r), 0n), False{}, z0, Equal.trans(Bool, Nat.is_eq(SW.value(r), 0n), Nat.is_eq(q, 0n), False{}, Equal.cong(Nat, Bool, z => Nat.is_eq(z, 0n), SW.value(r), q, ev), nz_of(52n, q, hz)))
  +e1 = Equal.cong(Bool, F.F64, t => F.pack(s, F.zero_e(E, t), r), X.is_zero(r), False{}, hzr)
  +hn = L.subst(Nat, z => {C.fits(63n, Nat.add(z, C.shift(52n, E))) == True{} : Bool}, q, SW.value(r), Equal.sym(Nat, SW.value(r), q, ev), hq)
  +e2 = pack_v(s, E, hE, r, hn)
  +e3 = Equal.cong(Nat, F.F64, z => bits(s, Nat.add(z, C.shift(52n, E))), SW.value(r), q, ev)
  Equal.trans(F.F64, F.pack(s, F.zero_e(E, X.is_zero(r)), r), F.pack(s, E, r), bits(s, Nat.add(q, C.shift(52n, E))), e1, Equal.trans(F.F64, F.pack(s, E, r), bits(s, Nat.add(SW.value(r), C.shift(52n, E))), bits(s, Nat.add(q, C.shift(52n, E))), e2, e3))

Uses (29):
  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_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend&name=bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend&name=nz_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend&name=pack_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend&name=rpw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=is_zero_value
  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=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=rne
  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/f64.bend&name=pack
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=rp_fin
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=zero_e
  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=add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=clear0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=is_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=lo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=shr