def ltf

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64divc.bend:37

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

37def ltf(+xl: U32, +xh: U32, +h: {Nat.is_eq(SF.efield(F.Bits{xl, xh}), 2047n) == False{} : Bool}) -> {Nat.is_lt(SF.efield(F.Bits{xl, xh}), 2047n) == True{} : Bool}:
38  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{}, h))