def main_j
bend-collections-laws-math@1.0.0.0 · proofs/math/random/float.bend:295
import bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend as Float
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/src/math/natural.bend as M
295def main_j(+one: Nat, +h1: {one == 1n : Nat}, +xv: Nat, +hx: {Nat.sub(SF.zb(), 53n) == xv : Nat}, +m: WU.U64, +np: Nat, +hM: {SW.value(m) == 1n+np : Nat}, +hf: {C.fits(53n, 1n+np) == True{} : Bool}, +j: Nat, +hbl: {M.bit_length(1n+np) == 1n+j : Nat}) -> {R.f53(m, X.clz(m)) == SF.round(False{}, 1n+np, xv) : F.F64}:
296 +hj = hj_of(np, j, hf, hbl)
297 Equal.trans(F.F64, R.f53(m, X.clz(m)), bits(X.shl(m, Nat.sub(52n, j)), Nat.add(j, 970n)), SF.round(False{}, 1n+np, xv),
298 impl_eq(m, np, hM, j, hj, hbl),
299 main_g(one, h1, xv, hx, m, np, hM, j, hj, hbl))