Nuprl Lemma : exp-positive
∀[n,x:ℕ+].  0 < x^n
Proof
Definitions occuring in Statement : 
exp: i^n
, 
nat_plus: 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_plus: ℕ+
, 
less_than: a < b
, 
squash: ↓T
, 
less_than': less_than'(a;b)
, 
true: True
, 
and: P ∧ Q
, 
prop: ℙ
, 
nat: ℕ
, 
le: A ≤ B
, 
subtract: n - m
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
top: Top
, 
guard: {T}
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
nat_plus_subtype_nat, 
member-less_than, 
primrec-wf-nat-plus, 
uall_wf, 
nat_plus_wf, 
int_formula_prop_wf, 
int_formula_prop_less_lemma, 
int_term_value_var_lemma, 
int_term_value_add_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
intformless_wf, 
itermVar_wf, 
itermAdd_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
exp_wf2, 
decidable__lt, 
nat_plus_properties, 
le_wf, 
false_wf, 
subtract_wf, 
exp_wf_nat_plus, 
mul_bounds_1b, 
less_than_wf, 
exp_step
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
dependent_set_memberEquality, 
natural_numberEquality, 
independent_pairFormation, 
imageMemberEquality, 
hypothesisEquality, 
baseClosed, 
hypothesis, 
setElimination, 
rename, 
lambdaFormation, 
because_Cache, 
dependent_functionElimination, 
addEquality, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
computeAll, 
equalityTransitivity, 
equalitySymmetry, 
applyEquality, 
independent_functionElimination
Latex:
\mforall{}[n,x:\mBbbN{}\msupplus{}].    0  <  x\^{}n
Date html generated:
2016_05_14-PM-04_26_47
Last ObjectModification:
2016_01_14-PM-11_36_35
Theory : num_thy_1
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