Nuprl Lemma : groupoid-nerve-filler2_wf
∀[G:Groupoid]. ∀[I:Cname List]. ∀[J:nameset(I) List]. ∀[x:nameset(I)]. ∀[i:ℕ2].
∀[box:open_box(cubical-nerve(cat(G));I;J;x;i)].
groupoid-nerve-filler2(cat(G);I;J;box) ∈ cubical-nerve(cat(G))(I) supposing 3 < ||box||
Proof
Definitions occuring in Statement :
groupoid-nerve-filler2: groupoid-nerve-filler2(C;I;J;box),
cubical-nerve: cubical-nerve(X),
open_box: open_box(X;I;J;x;i),
I-cube: X(I),
nameset: nameset(L),
coordinate_name: Cname,
groupoid-cat: cat(G),
groupoid: Groupoid,
length: ||as||,
list: T List,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
l_exists: (∃x∈L. P[x]),
exists: ∃x:A. B[x],
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
guard: {T},
int_seg: {i..j-},
nameset: nameset(L),
false: False,
coordinate_name: Cname,
int_upper: {i...},
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
prop: ℙ,
cons: [a / b],
bfalse: ff,
open_box: open_box(X;I;J;x;i),
subtype_rel: A ⊆r B,
groupoid-nerve-filler2: groupoid-nerve-filler2(C;I;J;box),
decidable: Dec(P),
name-morph: name-morph(I;J),
groupoid-cat: cat(G)
Lemmas referenced :
groupoid-edges-commute,
assert_wf,
not_wf,
and_wf,
nerve_box_edge_wf,
equal-wf-T-base,
nil_wf,
name-morph_wf,
extd-nameset-nil,
equal_wf,
top_wf,
null_wf3,
decidable__assert,
nerve_box_label_wf,
poset_functor_extend-is-functor,
cubical-nerve-I-cube,
groupoid_wf,
list_wf,
int_seg_wf,
coordinate_name_wf,
subtype_rel_list,
open_box_wf,
I-face_wf,
length_wf,
less_than_wf,
false_wf,
null_cons_lemma,
product_subtype_list,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_properties,
length_of_nil_lemma,
base_wf,
stuck-spread,
null_nil_lemma,
list-cases,
nameset_wf,
groupoid-cat_wf,
cubical-nerve_wf,
length-open_box-ge-3
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
sqequalRule,
productElimination,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
because_Cache,
setElimination,
rename,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
promote_hyp,
hypothesis_subsumption,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
inlFormation,
inrFormation,
dependent_set_memberEquality,
setEquality
Latex:
\mforall{}[G:Groupoid]. \mforall{}[I:Cname List]. \mforall{}[J:nameset(I) List]. \mforall{}[x:nameset(I)]. \mforall{}[i:\mBbbN{}2].
\mforall{}[box:open\_box(cubical-nerve(cat(G));I;J;x;i)].
groupoid-nerve-filler2(cat(G);I;J;box) \mmember{} cubical-nerve(cat(G))(I) supposing 3 < ||box||
Date html generated:
2016_06_16-PM-07_13_48
Last ObjectModification:
2016_01_18-PM-04_47_19
Theory : cubical!sets
Home
Index