def R_le

bend-collections-laws-math@1.0.0.0 · proofs/math/random/fround.bend:247

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/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sh.bend as SH

247def R_le(+one: Nat, +h1: {one == 1n : Nat}, +m: Nat, +hm: {C.fits(63n, m) == True{} : Bool}) -> {Nat.is_le(Nat.add(C.high(10n, m), C.high(10n, Nat.add(C.low(10n, m), 512n))), C.shift(53n, one)) == True{} : Bool}:
248  +t = C.high(10n, Nat.add(C.low(10n, m), 512n))
249  +ht = le1(t, SH.fits_high(10n, 1n, Nat.add(C.low(10n, m), 512n), fits_add1(10n, C.low(10n, m), 512n, WW.low_fits(10n, m), {==})))
250  +hq = WW.lt_one(53n, one, h1, C.high(10n, m), SH.fits_high(10n, 53n, m, hm))
251  N.le_trans(Nat.add(C.high(10n, m), C.high(10n, Nat.add(C.low(10n, m), 512n))), Nat.add(C.high(10n, m), 1n), C.shift(53n, one), N.le_add_left(t, 1n, C.high(10n, m), ht), succ_le(C.high(10n, m), C.shift(53n, one), hq))