def iw32

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:65

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/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/natural.bend as M
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/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW

65def iw32(+one: Nat, +h1: {one == 1n : Nat}, +nh: WU.U64, +h62: {C.fits(62n, SW.value(nh)) == True{} : Bool}, +h60: {C.fits(60n, SW.value(nh)) == False{} : Bool}) -> {C.fits(32n, SW.value(X.isqrt(nh))) == True{} : Bool}:
66  +l = N.lt_trans(M.isqrt(SW.value(nh)), C.shift(31n, one), C.shift(32n, one), iv31(one, h1, nh, h62, h60), p_lt(one, h1, 31n))
67  WW.fits_one(32n, one, h1, SW.value(X.isqrt(nh)), L.subst(Nat, z => {Nat.is_lt(z, C.shift(32n, one)) == True{} : Bool}, M.isqrt(SW.value(nh)), SW.value(X.isqrt(nh)), Equal.sym(Nat, SW.value(X.isqrt(nh)), M.isqrt(SW.value(nh)), iw_v(one, h1, nh, h62, h60)), l))