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
Home
Index