Nuprl Lemma : padic_subtype_basic-padic
∀[p:ℤ]. (padic(p) ⊆r basic-padic(p))
Proof
Definitions occuring in Statement :
padic: padic(p),
basic-padic: basic-padic(p),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
padic: padic(p),
basic-padic: basic-padic(p),
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
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,
p-units: p-units(p)
Lemmas referenced :
subtype_rel_product,
nat_wf,
ifthenelse_wf,
eq_int_wf,
p-adics_wf,
p-units_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
subtype_rel_self,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
instantiate,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
universeEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
dependent_functionElimination,
cumulativity,
independent_functionElimination,
voidElimination,
axiomEquality,
intEquality
Latex:
\mforall{}[p:\mBbbZ{}]. (padic(p) \msubseteq{}r basic-padic(p))
Date html generated:
2018_05_21-PM-03_26_01
Last ObjectModification:
2018_05_19-AM-08_22_55
Theory : rings_1
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