Nuprl Lemma : bpa-norm-padic
∀[p:ℕ+]. ∀[x:padic(p)]. (bpa-norm(p;x) = x ∈ padic(p))
Proof
Definitions occuring in Statement :
padic: padic(p),
bpa-norm: bpa-norm(p;x),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
padic: padic(p),
bpa-norm: bpa-norm(p;x),
member: t ∈ T,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
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 ,
squash: ↓T,
prop: ℙ,
nat_plus: ℕ+,
label: ...$L... t,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
subtype_rel: A ⊆r B,
eq_int: (i =z j),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
int_upper: {i...},
p-units: p-units(p),
int_seg: {i..j-},
lelt: i ≤ j < k,
p-adics: p-adics(p),
less_than: a < b,
p-unitize: p-unitize(p;a;n),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
equal_wf,
squash_wf,
true_wf,
nat_wf,
ifthenelse_wf,
p-adics_wf,
p-units_wf,
nat_properties,
nat_plus_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma,
le_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
subtype_rel_self,
iff_weakening_equal,
upper_subtype_nat,
false_wf,
nequal-le-implies,
zero-add,
p-adic-non-decreasing,
decidable__lt,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
le-add-cancel,
less_than_wf,
int_upper_properties,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
lelt_wf,
le_weakening2,
int_seg_wf,
exp_wf2,
int_seg_properties,
padic_wf,
nat_plus_wf,
set_subtype_base,
int_subtype_base,
greatest-p-zero-property,
decidable__equal_nat,
greatest-p-zero_wf,
equal-wf-T-base,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
cut,
introduction,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
productEquality,
instantiate,
because_Cache,
dependent_pairEquality,
dependent_functionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
dependent_set_memberEquality,
promote_hyp,
cumulativity,
imageMemberEquality,
baseClosed,
hypothesis_subsumption,
addEquality,
applyLambdaEquality,
functionExtensionality
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[x:padic(p)]. (bpa-norm(p;x) = x)
Date html generated:
2018_05_21-PM-03_26_17
Last ObjectModification:
2018_05_19-AM-08_24_07
Theory : rings_1
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