Nuprl Lemma : exp_wf2
∀[n:ℕ]. ∀[i:ℤ].  (i^n ∈ ℤ)
Proof
Definitions occuring in Statement : 
exp: i^n
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
int: ℤ
Definitions unfolded in proof : 
exp: i^n
, 
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
, 
eq_int: (i =z j)
, 
subtract: n - m
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
decidable: Dec(P)
, 
or: P ∨ Q
Lemmas referenced : 
nat_wf, 
eq_int_wf, 
ifthenelse_wf, 
int_term_value_subtract_lemma, 
int_formula_prop_not_lemma, 
itermSubtract_wf, 
intformnot_wf, 
subtract_wf, 
decidable__le, 
primrec-unroll, 
less_than_wf, 
ge_wf, 
int_formula_prop_wf, 
int_formula_prop_less_lemma, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_and_lemma, 
intformless_wf, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
nat_properties
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_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, 
independent_pairFormation, 
computeAll, 
independent_functionElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
unionElimination, 
multiplyEquality, 
because_Cache
Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[i:\mBbbZ{}].    (i\^{}n  \mmember{}  \mBbbZ{})
Date html generated:
2016_05_14-AM-07_34_22
Last ObjectModification:
2016_01_14-PM-09_53_56
Theory : int_2
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