def dw_nz

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:185

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/u32laws.bend as LW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqw.bend as QW

185def dw_nz(+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}) -> {U32.is_zero(U32.add(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))) == False{} : Bool}:
186  +e = Equal.trans(Bool, U32.is_zero(U32.add(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Nat.is_eq(v(U32.add(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), 0n), Nat.is_eq(Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), 0n), LW.zero_nat(U32.add(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Equal.cong(Nat, Bool, z => Nat.is_eq(z, 0n), v(U32.add(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), dw_v(one, h1, nh, h62, h60)))
187  +h = Equal.trans(Bool, Bool.not(Nat.is_eq(Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), 0n)), Nat.is_lt(0n, Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))), True{}, Equal.sym(Bool, Nat.is_lt(0n, Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh)))), Bool.not(Nat.is_eq(Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), 0n)), QW.ltz(Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))))), d_pos(one, h1, nh, h62, h60))
188  Equal.trans(Bool, U32.is_zero(U32.add(X.lo(X.isqrt(nh)), X.lo(X.isqrt(nh)))), Nat.is_eq(Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), 0n), False{}, e, not_t(Nat.is_eq(Nat.add(M.isqrt(SW.value(nh)), M.isqrt(SW.value(nh))), 0n), h))