def iv31

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:59

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

59def iv31(+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_lt(M.isqrt(SW.value(nh)), C.shift(31n, one)) == True{} : Bool}:
60  AQ.isqrt_lt(SW.value(nh), C.shift(31n, one), L.subst(Nat, z => {Nat.is_lt(SW.value(nh), z) == True{} : Bool}, C.shift(62n, one), Nat.mul(C.shift(31n, one), C.shift(31n, one)), Equal.sym(Nat, Nat.mul(C.shift(31n, one), C.shift(31n, one)), C.shift(62n, one), psq(one, h1, 31n)), vn62(one, h1, nh, h62)))