Nuprl Lemma : bpa-norm_wf_padic
∀[p:ℕ+]. ∀[x:basic-padic(p)]. (bpa-norm(p;x) ∈ padic(p))
Proof
Definitions occuring in Statement :
padic: padic(p),
bpa-norm: bpa-norm(p;x),
basic-padic: basic-padic(p),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
basic-padic: basic-padic(p),
nat_plus: ℕ+,
padic: padic(p),
all: ∀x:A. B[x],
implies: P ⇒ Q,
nat: ℕ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
ge: i ≥ j ,
int_upper: {i...},
bpa-norm: bpa-norm(p;x),
so_lambda: λ2x.t[x],
so_apply: x[s],
pi2: snd(t),
pi1: fst(t),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
p-adics: p-adics(p),
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
true: True,
int_seg: {i..j-},
nequal: a ≠ b ∈ T ,
lelt: i ≤ j < k,
p-units: p-units(p),
less_than: a < b,
squash: ↓T
Lemmas referenced :
basic-padic_wf,
nat_plus_wf,
bpa-norm_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
upper_subtype_nat,
false_wf,
nat_properties,
nequal-le-implies,
zero-add,
le_wf,
ifthenelse_wf,
p-adics_wf,
p-units_wf,
pi2_wf,
nat_wf,
pi1_wf,
int_upper_properties,
nat_plus_properties,
full-omega-unsat,
intformand_wf,
intformeq_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
decidable__lt,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
le-add-cancel,
less_than_wf,
int_seg_wf,
exp_wf2,
p-unitize_wf,
p-mul_wf,
p-int_wf,
subtract_wf,
int_seg_properties,
decidable__le,
intformnot_wf,
itermSubtract_wf,
intformless_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
equal-wf-T-base,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
rename,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
setElimination,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
independent_pairEquality,
lambdaFormation,
dependent_pairEquality,
natural_numberEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
because_Cache,
dependent_pairFormation,
promote_hyp,
instantiate,
independent_functionElimination,
voidElimination,
hypothesis_subsumption,
independent_pairFormation,
dependent_set_memberEquality,
universeEquality,
applyLambdaEquality,
lambdaEquality,
approximateComputation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
cumulativity,
applyEquality,
productEquality,
addEquality,
setEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[x:basic-padic(p)]. (bpa-norm(p;x) \mmember{} padic(p))
Date html generated:
2018_05_21-PM-03_26_07
Last ObjectModification:
2018_05_19-AM-08_23_30
Theory : rings_1
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