Roots.shrink: 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 148-150 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=148&end_line=150

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

# the interval shrinks: a step fits in the remaining fuel
def shrink(+x: Nat, +y: Nat, +f: Nat, +h: {Nat.is_lt(x, y) == True{} : Bool}, +hf: {Nat.is_le(y, 1n+f) == True{} : Bool}) -> {Nat.is_le(x, f) == True{} : Bool}:
  N.lt_succ_le(x, f, N.lt_le_trans(x, y, 1n+f, h, hf))

Uses (6):
  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_le
  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=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_succ_le