Natfuel.fbig: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/natfuel.bend as Natfuel
Lines 377-379 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/natfuel.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/natfuel.bend&start_line=377&end_line=379

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/spec/math/natural.bend as S

# 1 + k <= i gives 2^k <= i!
def fbig(+k: Nat, +i: Nat, +h: {Nat.is_le(1n+k, i) == True{} : Bool}) -> {Nat.is_le(C.pow2(k), S.factorial(i)) == True{} : Bool}:
  N.le_trans(C.pow2(k), S.factorial(1n+k), S.factorial(i), pf_le(k), fmono(1n+k, i, h))

Uses (8):
  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=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/natfuel.bend&name=fmono
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/natfuel.bend&name=pf_le
  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/spec/math/natural.bend&name=factorial