def nlt

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64rint.bend:169

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/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend as FR

169# V < 2^k is not above 2^k
170def nlt(+k: Nat, +one: Nat, +h1: {one == 1n : Nat}, +V: Nat, +hf: {C.fits(k, V) == True{} : Bool}) -> {Nat.is_lt(C.shift(k, one), V) == False{} : Bool}:
171  +hl = Equal.trans(Bool, Nat.is_lt(V, C.shift(k, one)), C.fits(k, V), True{}, FR.lt_fit(k, one, h1, V), hf)
172  N.le_not_lt(C.shift(k, one), V, N.lt_le(V, C.shift(k, one), hl))