def fbig

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/natfuel.bend:377

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

377# 1 + k <= i gives 2^k <= i!
378def 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}:
379  N.le_trans(C.pow2(k), S.factorial(1n+k), S.factorial(i), pf_le(k), fmono(1n+k, i, h))