Nuprl Lemma : tuple_wf_ntuple
∀[n:ℕ]. ∀[F:Top]. (tuple(n;i.F[i]) ∈ n-tuple(n))
Proof
Definitions occuring in Statement :
tuple: tuple(n;i.F[i]),
n-tuple: n-tuple(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
member: t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
top: Top,
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
ge: i ≥ j
Lemmas referenced :
false_wf,
le_wf,
it_wf,
top_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_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,
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,
nat_properties,
ge_wf,
less_than_wf,
n-tuple-decomp,
tuple-decomp,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
equalityElimination,
productElimination,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
independent_pairEquality,
setElimination,
rename,
intWeakElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[F:Top]. (tuple(n;i.F[i]) \mmember{} n-tuple(n))
Date html generated:
2017_04_17-AM-09_29_18
Last ObjectModification:
2017_02_27-PM-05_29_11
Theory : tuples
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