Proof.iroot_lt_succ: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend as Proof
Lines 127-129 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend&start_line=127&end_line=129

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/roots.bend as RT

def iroot_lt_succ(+n: Nat, +kp: Nat, +r: Nat, +h: {M.iroot(n, 1n+kp) == Done{r} : Result<&2, &2, M.MathError, Nat>}) -> S.Iroot.lt_succ(n, kp, r, h):
  %iroot_value(n, kp, r, h) : {Nat.is_lt(n, Nat.pow(1n+_, 1n+kp)) == True{} : Bool}
  RT.lt_succ_iroot(n, kp)

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend&name=iroot_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/roots.bend&name=lt_succ_iroot
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=Iroot.lt_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=MathError
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=iroot