def div_v

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqr.bend:382

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/src/math/natural.bend as M

382def div_v(+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}, +e: Nat, +x: Nat, +hx: {Nat.add(x, 2180n) == e : Nat}, p: WU.U64 & U32, +hq: {SW.value(X.fst_q(p)) == Nat.div(C.shift(32n, Nat.sub(SW.value(nh), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))))), Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))) : Nat}, +hu: {v(X.snd_r(p)) == Nat.mod(C.shift(32n, Nat.sub(SW.value(nh), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))))), Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))) : Nat}) -> {F.sq_div(e, X.lo(X.isqrt(nh)), p) == SF.round(False{}, SW.jam(M.isqrt(C.shift(64n, SW.value(nh))), SF.b2n(Bool.not(Nat.is_eq(Nat.mul(M.isqrt(C.shift(64n, SW.value(nh))), M.isqrt(C.shift(64n, SW.value(nh)))), C.shift(64n, SW.value(nh)))))), x) : F.F64}:
383  match p:
384    case Tuple{+qq, +uu}:
385      cl_v(one, h1, nh, h62, h60, e, x, hx, qq, uu, hq, hu, U32.is_zero(X.hi(qq)), {==})