def value_z
bend-collections-laws-math@1.0.0.0 · proofs/math/random/float.bend:342
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
342def value_z(+x: WU.U64, +n: Nat, +hn: {C.low(53n, SW.value(x)) == n : Nat}, +xv: Nat, +hv: {SW.value(mm(x)) == 0n : Nat}) -> {R.to_float(x) == SF.round(False{}, n, xv) : F.F64}:
343 +h0 = Equal.trans(Nat, n, C.low(53n, SW.value(x)), 0n, Equal.sym(Nat, C.low(53n, SW.value(x)), n, hn), hl_of(x, 0n, hv))
344 %Equal.sym(Nat, n, 0n, h0) : {R.to_float(x) == SF.round(False{}, _, xv) : F.F64}
345 %Equal.sym(Bool, X.is_zero(mm(x)), Nat.is_eq(0n, 0n), iz(mm(x), 0n, hv)) : {R.f53_z(mm(x), _) == SF.round(False{}, 0n, xv) : F.F64}
346 Equal.trans(F.F64, R.f53_z(mm(x), Nat.is_eq(0n, 0n)), SF.zero(False{}), SF.round(False{}, 0n, xv), {==}, Equal.sym(F.F64, SF.round(False{}, 0n, xv), SF.zero(False{}), round0(xv)))