Nuprl Lemma : exp_wf3
∀[v:ℤ-o]. ∀[n:ℕ]. (v^n ∈ ℤ-o)
Proof
Definitions occuring in Statement :
exp: i^n,
int_nzero: ℤ-o,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
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,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
sq_type: SQType(T),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B
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,
primrec-unroll,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
nequal_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_entire_a,
int_nzero_wf,
int_nzero_properties,
intformeq_wf,
int_formula_prop_eq_lemma,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
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,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
addLevel,
instantiate,
cumulativity,
baseClosed,
unionElimination,
because_Cache,
equalityElimination,
productElimination,
promote_hyp,
multiplyEquality,
applyEquality,
applyLambdaEquality,
baseApply,
closedConclusion
Latex:
\mforall{}[v:\mBbbZ{}\msupminus{}\msupzero{}]. \mforall{}[n:\mBbbN{}]. (v\^{}n \mmember{} \mBbbZ{}\msupminus{}\msupzero{})
Date html generated:
2017_04_14-AM-09_22_12
Last ObjectModification:
2017_02_27-PM-03_57_47
Theory : int_2
Home
Index