Nuprl Lemma : rexp-approx-lemma
∀N:ℕ+. (∃k:ℕ [(N ≤ (4^k * 3 * (k)!))])
Proof
Definitions occuring in Statement :
fact: (n)!,
exp: i^n,
nat_plus: ℕ+,
nat: ℕ,
le: A ≤ B,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
multiply: n * m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
so_apply: x[s],
uimplies: b supposing a,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
subtype_rel: A ⊆r B,
sq_exists: ∃x:A [B[x]],
nat: ℕ
Lemmas referenced :
genfact-inv_wf,
nat_plus_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-less_than,
nat_plus_subtype_nat,
subtype_rel_sets_simple,
nat_wf,
le_wf,
genfact_wf,
istype-nat,
exp_wf2,
fact_wf,
mul-swap,
exp-fact-as-genfact,
istype-le,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality_alt,
multiplyEquality,
closedConclusion,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
inhabitedIsType,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
dependent_set_memberEquality_alt,
imageMemberEquality,
baseClosed,
applyEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}N:\mBbbN{}\msupplus{}. (\mexists{}k:\mBbbN{} [(N \mleq{} (4\^{}k * 3 * (k)!))])
Date html generated:
2019_10_30-AM-11_40_46
Last ObjectModification:
2019_02_08-PM-02_06_36
Theory : reals_2
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