def mm_v

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:152

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/math/typed/w64mul.bend as W64M

152def mm_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.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))) == Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))) : Nat}:
153  Equal.trans(Nat, SW.value(X.mul32(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Nat.mul(v(X.lo(X.isqrt(nh))), v(X.lo(X.isqrt(nh)))), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), W64M.mul32_value(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh))), Equal.trans(Nat, Nat.mul(v(X.lo(X.isqrt(nh))), v(X.lo(X.isqrt(nh)))), Nat.mul(M.isqrt(SW.value(nh)), v(X.lo(X.isqrt(nh)))), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), Equal.cong(Nat, Nat, z => Nat.mul(z, v(X.lo(X.isqrt(nh)))), v(X.lo(X.isqrt(nh))), M.isqrt(SW.value(nh)), s_v(one, h1, nh, h62, h60)), Equal.cong(Nat, Nat, z => Nat.mul(M.isqrt(SW.value(nh)), z), v(X.lo(X.isqrt(nh))), M.isqrt(SW.value(nh)), s_v(one, h1, nh, h62, h60))))