Roots.hi_pos: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/roots.bend as Roots
Lines 222-224 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/roots.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/roots.bend&start_line=222&end_line=224

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-math@1.0.0.0/src/math/pow2.bend as P2
import bend-collections-laws-math@1.0.0.0/proofs/math/pow2/pow2.bend as PP

def hi_pos(+a: Nat) -> {Nat.is_lt(0n, P2.pow2t(a)) == True{} : Bool}:
  %Equal.sym(Nat, P2.pow2t(a), SC.pow2(a), PP.same(a)) : {Nat.is_lt(0n, _) == True{} : Bool}
  N.succ_le_lt(0n, SC.pow2(a), N.pow2_pos(a))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=pow2_pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_le_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/pow2/pow2.bend&name=same
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=pow2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/pow2.bend&name=pow2t