def s_lo

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:88

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/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/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqa.bend as AQ

88def s_lo(+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}) -> {Nat.is_le(C.shift(32n, M.isqrt(SW.value(nh))), M.isqrt(C.shift(64n, SW.value(nh)))) == True{} : Bool}:
89  AQ.isqrt_ge(C.shift(64n, SW.value(nh)), C.shift(32n, M.isqrt(SW.value(nh))), L.subst(Nat, z => {Nat.is_le(z, C.shift(64n, SW.value(nh))) == True{} : Bool}, C.shift(32n, C.shift(32n, Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))))), Nat.mul(C.shift(32n, M.isqrt(SW.value(nh))), C.shift(32n, M.isqrt(SW.value(nh)))), Equal.sym(Nat, Nat.mul(C.shift(32n, M.isqrt(SW.value(nh))), C.shift(32n, M.isqrt(SW.value(nh)))), C.shift(32n, C.shift(32n, Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))))), AQ.sh_sq(32n, M.isqrt(SW.value(nh)))), L.subst(Nat, z => {Nat.is_le(C.shift(32n, C.shift(32n, Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))))), z) == True{} : Bool}, C.shift(32n, C.shift(32n, SW.value(nh))), C.shift(64n, SW.value(nh)), Equal.sym(Nat, C.shift(64n, SW.value(nh)), C.shift(32n, C.shift(32n, SW.value(nh))), nn_eq(nh)), AQ.le_sh2(32n, Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), SW.value(nh), AQ.isl(SW.value(nh))))))