Nuprl Lemma : update-tuple_wf
∀[L:Type List]. ∀[n:ℕ]. ∀[x:tuple-type(L)]. ∀[y:L[n]]. (update-tuple(||L||;x;n;y) ∈ tuple-type(L)) supposing n < ||L||
Proof
Definitions occuring in Statement :
update-tuple: update-tuple(len;x;n;y),
tuple-type: tuple-type(L),
select: L[n],
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
or: P ∨ Q,
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
update-tuple: update-tuple(len;x;n;y),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
bfalse: ff,
cons: [a / b],
colength: colength(L),
decidable: Dec(P),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
int_upper: {i...},
nequal: a ≠ b ∈ T ,
pi2: snd(t),
pi1: fst(t)
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_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,
ge_wf,
less_than_wf,
select_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
length_wf,
tuple-type_wf,
nat_wf,
equal-wf-T-base,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list_wf,
list-cases,
tupletype_nil_lemma,
length_of_nil_lemma,
stuck-spread,
base_wf,
product_subtype_list,
spread_cons_lemma,
itermAdd_wf,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
equal_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
tupletype_cons_lemma,
length_of_cons_lemma,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
false_wf,
nequal-le-implies,
zero-add,
int_upper_properties,
unit_wf2,
null_nil_lemma,
subtype_rel-equal,
cons_wf,
nil_wf,
length-singleton,
select-cons-hd,
null_cons_lemma,
ifthenelse_wf,
null_wf,
assert_of_null,
non_neg_length,
add-subtract-cancel,
pi2_wf,
decidable__lt,
add-is-int-iff,
select-cons-tl
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
because_Cache,
applyLambdaEquality,
applyEquality,
unionElimination,
baseClosed,
promote_hyp,
hypothesis_subsumption,
productElimination,
dependent_set_memberEquality,
addEquality,
cumulativity,
imageElimination,
equalityElimination,
productEquality,
independent_pairEquality,
pointwiseFunctionality,
baseApply,
closedConclusion
Latex:
\mforall{}[L:Type List]. \mforall{}[n:\mBbbN{}]. \mforall{}[x:tuple-type(L)].
\mforall{}[y:L[n]]. (update-tuple(||L||;x;n;y) \mmember{} tuple-type(L)) supposing n < ||L||
Date html generated:
2017_04_17-AM-09_29_32
Last ObjectModification:
2017_02_27-PM-05_30_28
Theory : tuples
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