Nuprl Lemma : exp-greater
∀[x:{2...}]. ∀[n:ℕ]. n < x^n
Proof
Definitions occuring in Statement :
exp: i^n
,
int_upper: {i...}
,
nat: ℕ
,
less_than: a < b
,
uall: ∀[x:A]. B[x]
,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
nat: ℕ
,
implies: P
⇒ Q
,
false: False
,
ge: i ≥ j
,
uimplies: b supposing a
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
not: ¬A
,
all: ∀x:A. B[x]
,
top: Top
,
and: P ∧ Q
,
prop: ℙ
,
guard: {T}
,
int_upper: {i...}
,
less_than: a < b
,
squash: ↓T
,
less_than': less_than'(a;b)
,
true: True
,
decidable: Dec(P)
,
or: P ∨ Q
,
nat_plus: ℕ+
,
le: A ≤ B
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
uiff: uiff(P;Q)
,
subtype_rel: A ⊆r B
,
sq_type: SQType(T)
,
subtract: n - m
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
member-less_than,
exp_wf2,
int_upper_properties,
exp0_lemma,
le_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
exp_step,
mul_preserves_lt,
decidable__lt,
false_wf,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
itermMultiply_wf,
int_term_value_mul_lemma,
not-equal-2,
less-iff-le,
add-associates,
add-zero,
le-add-cancel2,
condition-implies-le,
minus-add,
add-swap,
minus-minus,
minus-one-mul,
minus-one-mul-top,
nat_plus_wf,
equal_wf,
subtract-add-cancel,
nat_wf,
int_upper_wf,
nat_plus_properties,
itermAdd_wf,
int_term_value_add_lemma,
primrec-wf-nat-plus
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
imageMemberEquality,
baseClosed,
dependent_set_memberEquality,
because_Cache,
unionElimination,
productElimination,
applyEquality,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
multiplyEquality,
addEquality,
minusEquality,
imageElimination
Latex:
\mforall{}[x:\{2...\}]. \mforall{}[n:\mBbbN{}]. n < x\^{}n
Date html generated:
2017_04_17-AM-09_45_07
Last ObjectModification:
2017_02_27-PM-05_39_23
Theory : num_thy_1
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