def dw_value

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqr.bend:260

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/nat.bend as N
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

260def dw_value(+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}, +hBA: {Nat.is_lt(C.shift(32n, v(u)), Nat.mul(v(q), v(q))) == True{} : Bool}) -> {SW.value(X.sub(X.mul32(q, q), WU.U64{0, u})) == Nat.sub(Nat.mul(v(q), v(q)), C.shift(32n, v(u))) : Nat}:
261  +h = L.subst(Nat, z => {Nat.is_le(C.shift(32n, v(u)), z) == True{} : Bool}, Nat.mul(v(q), v(q)), SW.value(X.mul32(q, q)), Equal.sym(Nat, SW.value(X.mul32(q, q)), Nat.mul(v(q), v(q)), bv_q(q)), N.lt_le(C.shift(32n, v(u)), Nat.mul(v(q), v(q)), hBA))
262  Equal.trans(Nat, SW.value(X.sub(X.mul32(q, q), WU.U64{0, u})), Nat.sub(SW.value(X.mul32(q, q)), SW.value(WU.U64{0, u})), Nat.sub(Nat.mul(v(q), v(q)), C.shift(32n, v(u))), WA.sub_value(X.mul32(q, q), WU.U64{0, u}, h), Equal.cong(Nat, Nat, z => Nat.sub(z, C.shift(32n, v(u))), SW.value(X.mul32(q, q)), Nat.mul(v(q), v(q)), bv_q(q)))