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
Home
Index