Nuprl Lemma : tuple-type-subtype-n-tuple
∀[L:Type List]. ∀[n:ℕ].  tuple-type(L) ⊆r n-tuple(n) supposing ||L|| = n ∈ ℤ
Proof
Definitions occuring in Statement : 
n-tuple: n-tuple(n)
, 
tuple-type: tuple-type(L)
, 
length: ||as||
, 
list: T List
, 
nat: ℕ
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
int: ℤ
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
sq_type: SQType(T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
n-tuple: n-tuple(n)
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
nat: ℕ
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
top: Top
, 
squash: ↓T
, 
true: True
, 
iff: P 
⇐⇒ Q
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
less_than: a < b
, 
ge: i ≥ j 
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
Lemmas referenced : 
subtype_base_sq, 
int_subtype_base, 
equal_wf, 
length_wf, 
nat_wf, 
list_wf, 
subtype_rel_tuple-type, 
map_wf, 
int_seg_wf, 
top_wf, 
upto_wf, 
map-length, 
length_upto, 
length_wf_nat, 
squash_wf, 
true_wf, 
iff_weakening_equal, 
select-map, 
subtype_rel_list, 
lelt_wf, 
select_wf, 
int_seg_properties, 
nat_properties, 
decidable__le, 
satisfiable-full-omega-tt, 
intformand_wf, 
intformnot_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_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_wf, 
decidable__lt, 
intformless_wf, 
int_formula_prop_less_lemma
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
thin, 
instantiate, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
intEquality, 
independent_isectElimination, 
hypothesis, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
sqequalRule, 
axiomEquality, 
universeEquality, 
hypothesisEquality, 
setElimination, 
rename, 
isect_memberEquality, 
because_Cache, 
natural_numberEquality, 
lambdaEquality, 
voidElimination, 
voidEquality, 
applyEquality, 
imageElimination, 
imageMemberEquality, 
baseClosed, 
productElimination, 
independent_pairFormation, 
lambdaFormation, 
dependent_set_memberEquality, 
unionElimination, 
dependent_pairFormation, 
int_eqEquality, 
computeAll
Latex:
\mforall{}[L:Type  List].  \mforall{}[n:\mBbbN{}].    tuple-type(L)  \msubseteq{}r  n-tuple(n)  supposing  ||L||  =  n
Date html generated:
2017_04_17-AM-09_29_10
Last ObjectModification:
2017_02_27-PM-05_29_21
Theory : tuples
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