def hS

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqr.bend:227

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/nat.bend as N

227def hS(+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}, +q: U32, +u: U32, +hc: {Nat.add(Nat.mul(v(q), Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))), v(u)) == C.shift(32n, Nat.sub(SW.value(nh), Nat.mul(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))))) : Nat}, +hU: {Nat.is_le(v(u), Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))) == True{} : Bool}, +hQ: {Nat.is_lt(v(q), C.shift(32n, one)) == True{} : Bool}) -> {Nat.add(v(q), C.shift(32n, M.isqrt(SW.value(nh)))) == 2n+Nat.sub(Nat.add(v(q), C.shift(32n, M.isqrt(SW.value(nh)))), 2n) : Nat}:
228  Equal.sym(Nat, 2n+Nat.sub(Nat.add(v(q), C.shift(32n, M.isqrt(SW.value(nh)))), 2n), Nat.add(v(q), C.shift(32n, M.isqrt(SW.value(nh)))), N.sub_add(Nat.add(v(q), C.shift(32n, M.isqrt(SW.value(nh)))), 2n, s0_2(one, h1, nh, h62, h60, q, u, hc, hU, hQ)))