def big_nat

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64conv.bend:113

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/f64.bend as SF
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/f64.bend as F
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/num.bend as NE
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/math/typed/w64clz.bend as CZ
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bl.bend as BL

113def big_nat(+s: Bool, +w: WU.U64, +k: Nat, +hz: {Nat.is_eq(SW.value(w), 0n) == False{} : Bool}, +hw: {C.fits(53n, SW.value(w)) == True{} : Bool}) -> {SF.rv64(F.tu_big(s, w, k, Nat.is_le(Nat.add(k, Nat.sub(64n, X.clz(w))), 64n))) == TN(s, C.shift(k, SW.value(w))) : Result<&2, &2, NE.NumError, Nat>}:
114  +V = SW.value(w)
115  +B = M.bit_length(V)
116  +hB = N.le_trans(B, 53n, 64n, BL.bl_le(53n, V, hw, Nat.is_le(B, 53n), {==}), {==})
117  +eb = Equal.trans(Nat, Nat.sub(64n, X.clz(w)), Nat.sub(64n, Nat.sub(64n, B)), B, Equal.cong(Nat, Nat, t => Nat.sub(64n, t), X.clz(w), Nat.sub(64n, B), CZ.clz_value(w)), subsub(64n, B, hB))
118  +e1 = Equal.cong(Nat, Result<&2, &2, NE.NumError, Nat>, t => SF.rv64(F.tu_big(s, w, k, Nat.is_le(Nat.add(k, t), 64n))), Nat.sub(64n, X.clz(w)), B, eb)
119  Equal.trans(Result<&2, &2, NE.NumError, Nat>, SF.rv64(F.tu_big(s, w, k, Nat.is_le(Nat.add(k, Nat.sub(64n, X.clz(w))), 64n))), SF.rv64(F.tu_big(s, w, k, Nat.is_le(Nat.add(k, B), 64n))), TN(s, C.shift(k, V)), e1, big_c(s, w, k, hz, Nat.is_le(Nat.add(k, B), 64n), {==}))