Nuprl Lemma : map-tuple_wf
∀[n:ℕ]. ∀[A,B:Type List].
∀[f:⋂i:ℕn. (A[i] ⟶ B[i])]. ∀[t:tuple-type(A)]. (map-tuple(n;f;t) ∈ tuple-type(B))
supposing (||A|| = n ∈ ℤ) ∧ (||B|| = n ∈ ℤ)
Proof
Definitions occuring in Statement :
map-tuple: map-tuple(len;f;t),
tuple-type: tuple-type(L),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
or: P ∨ Q,
map-tuple: map-tuple(len;f;t),
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
le: A ≤ B,
bool: 𝔹,
unit: Unit,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
less_than': less_than'(a;b),
decidable: Dec(P),
pi1: fst(t),
pi2: snd(t),
squash: ↓T,
cand: A c∧ B
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
list-cases,
tupletype_nil_lemma,
stuck-spread,
istype-base,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
non_neg_length,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
tupletype_cons_lemma,
null_wf,
eqtt_to_assert,
assert_of_null,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
equal-wf-T-base,
list_wf,
tuple-type_wf,
int_seg_wf,
int_seg_properties,
length_wf_nat,
set_subtype_base,
le_wf,
int_subtype_base,
subtract-1-ge-0,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
null_nil_lemma,
btrue_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
iff_imp_equal_bool,
true_wf,
istype-false,
le_weakening2,
nil_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__equal_int,
add-is-int-iff,
itermSubtract_wf,
int_term_value_subtract_lemma,
false_wf,
subtract_wf,
add-member-int_seg2,
equal_wf,
squash_wf,
istype-universe,
select_cons_tl,
cons_wf,
decidable__lt,
length_wf,
subtype_rel_self,
iff_weakening_equal,
subtype_rel_dep_function,
select_wf,
add-subtract-cancel,
subtype_rel-equal,
add-associates,
add-swap,
add-commutes,
zero-add,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
Error :lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
universeEquality,
instantiate,
unionElimination,
baseClosed,
promote_hyp,
hypothesis_subsumption,
equalityElimination,
because_Cache,
Error :equalityIsType1,
cumulativity,
Error :equalityIsType3,
Error :isectIsType,
Error :equalityIsType4,
applyEquality,
intEquality,
Error :equalityIsType2,
baseApply,
closedConclusion,
Error :dependent_set_memberEquality_alt,
Error :productIsType,
applyLambdaEquality,
pointwiseFunctionality,
imageElimination,
functionEquality,
addEquality,
imageMemberEquality,
minusEquality,
independent_pairEquality,
Error :functionIsType
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[A,B:Type List].
\mforall{}[f:\mcap{}i:\mBbbN{}n. (A[i] {}\mrightarrow{} B[i])]. \mforall{}[t:tuple-type(A)]. (map-tuple(n;f;t) \mmember{} tuple-type(B))
supposing (||A|| = n) \mwedge{} (||B|| = n)
Date html generated:
2019_06_20-PM-02_03_18
Last ObjectModification:
2018_10_08-PM-06_21_19
Theory : tuples
Home
Index