def w_v

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:155

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/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqa.bend as AQ

155def w_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}) -> {SW.value(X.sub(nh, X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh))))) == Nat.sub(SW.value(nh), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))) : Nat}:
156  +h = L.subst(Nat, z => {Nat.is_le(z, SW.value(nh)) == True{} : Bool}, Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), SW.value(X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Equal.sym(Nat, SW.value(X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), mm_v(one, h1, nh, h62, h60)), AQ.isl(SW.value(nh)))
157  Equal.trans(Nat, SW.value(X.sub(nh, X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh))))), Nat.sub(SW.value(nh), SW.value(X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh))))), Nat.sub(SW.value(nh), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))), WA.sub_value(nh, X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh))), h), Equal.cong(Nat, Nat, z => Nat.sub(SW.value(nh), z), SW.value(X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), mm_v(one, h1, nh, h62, h60)))