Nuprl Lemma : pa-int_wf
∀[p:{2...}]. ∀[k:ℤ]. (k(p) ∈ padic(p))
Proof
Definitions occuring in Statement :
pa-int: k(p),
padic: padic(p),
int_upper: {i...},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pa-int: k(p),
padic: padic(p),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
int_upper: {i...},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
true: True,
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
false_wf,
le_wf,
p-int_wf,
decidable__lt,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
less_than_wf,
p-adics_wf,
ifthenelse_wf,
eq_int_wf,
p-units_wf,
int_upper_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_pairEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
because_Cache,
productElimination,
dependent_functionElimination,
unionElimination,
voidElimination,
independent_functionElimination,
independent_isectElimination,
applyEquality,
lambdaEquality,
instantiate,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality
Latex:
\mforall{}[p:\{2...\}]. \mforall{}[k:\mBbbZ{}]. (k(p) \mmember{} padic(p))
Date html generated:
2018_05_21-PM-03_26_46
Last ObjectModification:
2018_05_19-AM-08_24_03
Theory : rings_1
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