def lt2047

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64cmp.bend:178

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/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB

178def lt2047(+xl: U32, +xh: U32, +hi: {SF.is_inf(F.Bits{xl, xh}) == False{} : Bool}, +hn: {SF.is_nan(F.Bits{xl, xh}) == False{} : Bool}) -> {Nat.is_lt(SF.efield(F.Bits{xl, xh}), 2047n) == True{} : Bool}:
179  +a = nl(Nat.is_eq(SF.efield(F.Bits{xl, xh}), 2047n), Nat.is_eq(SF.frac(F.Bits{xl, xh}), 0n), hi, hn)
180  Equal.trans(Bool, Nat.is_lt(SF.efield(F.Bits{xl, xh}), 2047n), Bool.not(Nat.is_eq(SF.efield(F.Bits{xl, xh}), 2047n)), True{}, FB.lt_ne(SF.efield(F.Bits{xl, xh}), 2047n, WW.low_lt(11n, C.high(20n, v(xh)))), Equal.cong(Bool, Bool, t => Bool.not(t), Nat.is_eq(SF.efield(F.Bits{xl, xh}), 2047n), False{}, a))