Nuprl Lemma : cubical-interval-filler_wf
cubical-interval-filler() ∈ I:(Cname List)
⟶ J:(nameset(I) List)
⟶ x:nameset(I)
⟶ i:ℕ2
⟶ open_box(cubical-interval();I;J;x;i)
⟶ cubical-interval()(I)
Proof
Definitions occuring in Statement :
cubical-interval-filler: cubical-interval-filler(),
open_box: open_box(X;I;J;x;i),
cubical-interval: cubical-interval(),
I-cube: X(I),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
cubical-interval-filler: cubical-interval-filler(),
member: t ∈ T,
cubical-interval: cubical-interval(),
I-cube: X(I),
all: ∀x:A. B[x],
top: Top,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
nameset: nameset(L),
open_box: open_box(X;I;J;x;i),
cons: [a / b],
l_exists: (∃x∈L. P[x]),
int_seg: {i..j-},
coordinate_name: Cname,
int_upper: {i...},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
so_lambda: λ2x.t[x],
sq_stable: SqStable(P),
squash: ↓T,
decidable: Dec(P),
le: A ≤ B,
so_apply: x[s],
cand: A c∧ B,
nat: ℕ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
less_than': less_than'(a;b),
true: True,
listp: A List+,
name-morph: name-morph(I;J)
Lemmas referenced :
ob_pair_lemma,
null_wf3,
subtype_rel_list,
top_wf,
bool_wf,
eqtt_to_assert,
assert_of_null,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
equal-wf-T-base,
list_wf,
nameset_wf,
open_box_wf,
cubical-interval_wf,
coordinate_name_wf,
int_seg_wf,
I-face_wf,
list-cases,
product_subtype_list,
reduce_hd_cons_lemma,
length_of_nil_lemma,
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
I-cube_wf,
list-diff_wf,
cname_deq_wf,
cons_wf,
nil_wf,
isect_subtype_rel_trivial,
name-morph_wf,
subtype_rel-equal,
cubical-set_wf,
decidable__le,
le_wf,
face-cube_wf,
subtype_rel_dep_function,
face-dimension_wf,
name-morph_subtype,
nameset_subtype,
list-diff-subset,
subtype_rel_self,
hd_wf,
l_member_wf,
list-subtype,
listp_properties,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__lt,
false_wf,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
less_than_wf,
length_wf,
get_face_wf,
extd-nameset-nil,
face-name_wf,
cubical-interval-ap_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
baseClosed,
setElimination,
rename,
natural_numberEquality,
hypothesis_subsumption,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
isectEquality,
universeEquality,
functionEquality,
imageMemberEquality,
imageElimination,
dependent_set_memberEquality,
setEquality,
addEquality,
minusEquality,
productEquality,
independent_pairEquality
Latex:
cubical-interval-filler() \mmember{} I:(Cname List)
{}\mrightarrow{} J:(nameset(I) List)
{}\mrightarrow{} x:nameset(I)
{}\mrightarrow{} i:\mBbbN{}2
{}\mrightarrow{} open\_box(cubical-interval();I;J;x;i)
{}\mrightarrow{} cubical-interval()(I)
Date html generated:
2017_10_05-AM-10_26_44
Last ObjectModification:
2017_07_28-AM-11_23_01
Theory : cubical!sets
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