Nuprl Lemma : append-tuple_wf
∀[L1,L2:Type List]. ∀[x:tuple-type(L1)]. ∀[y:tuple-type(L2)]. (append-tuple(||L1||;||L2||;x;y) ∈ tuple-type(L1 @ L2))
Proof
Definitions occuring in Statement :
append-tuple: append-tuple(n;m;x;y),
tuple-type: tuple-type(L),
length: ||as||,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uiff: uiff(P;Q),
unit: Unit,
bool: 𝔹,
less_than': less_than'(a;b),
squash: ↓T,
less_than: a < b,
sq_type: SQType(T),
so_apply: x[s],
so_lambda: λ2x.t[x],
it: ⋅,
nil: [],
decidable: Dec(P),
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
colength: colength(L),
cons: [a / b],
btrue: tt,
subtract: n - m,
eq_int: (i =z j),
bfalse: ff,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
lt_int: i <z j,
le_int: i ≤z j,
append-tuple: append-tuple(n;m;x;y),
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
append: as @ bs,
or: P ∨ Q,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
top: Top,
not: ¬A,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
true: True,
nat_plus: ℕ+,
le: A ≤ B,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
ifthenelse_wf,
assert_of_null,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
bool_wf,
append_wf,
null_wf,
length_of_cons_lemma,
list_ind_cons_lemma,
tupletype_cons_lemma,
decidable__equal_int,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
equal_wf,
le_wf,
int_formula_prop_not_lemma,
intformnot_wf,
decidable__le,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
itermAdd_wf,
intformeq_wf,
spread_cons_lemma,
product_subtype_list,
unit_wf2,
length_of_nil_lemma,
list_ind_nil_lemma,
tupletype_nil_lemma,
list-cases,
less_than_irreflexivity,
less_than_transitivity1,
colength_wf_list,
nat_wf,
equal-wf-T-base,
list_wf,
tuple-type_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
null_cons_lemma,
length_wf,
null_nil_lemma,
add_nat_plus,
length_wf_nat,
decidable__lt,
full-omega-unsat,
istype-int,
istype-void,
istype-less_than,
nat_plus_properties,
add-is-int-iff,
false_wf,
le_int_wf,
assert_of_le_int,
non_neg_length,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
istype-le,
btrue_neq_bfalse,
iff_imp_equal_bool,
iff_functionality_wrt_iff,
iff_weakening_equal,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
add-subtract-cancel
Rules used in proof :
productEquality,
equalityElimination,
imageElimination,
cumulativity,
baseClosed,
addEquality,
dependent_set_memberEquality,
applyLambdaEquality,
productElimination,
hypothesis_subsumption,
promote_hyp,
unionElimination,
because_Cache,
applyEquality,
universeEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_functionElimination,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
natural_numberEquality,
intWeakElimination,
sqequalRule,
rename,
setElimination,
hypothesis,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaFormation,
thin,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
Error :dependent_set_memberEquality_alt,
approximateComputation,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
Error :universeIsType,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
pointwiseFunctionality,
baseApply,
closedConclusion,
Error :equalityIstype,
independent_pairEquality
Latex:
\mforall{}[L1,L2:Type List]. \mforall{}[x:tuple-type(L1)]. \mforall{}[y:tuple-type(L2)].
(append-tuple(||L1||;||L2||;x;y) \mmember{} tuple-type(L1 @ L2))
Date html generated:
2019_06_20-PM-02_03_35
Last ObjectModification:
2018_12_07-AM-01_29_03
Theory : tuples
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