Nuprl Lemma : cu_filler_1_wf
∀[I:Cname List]. ∀[J:nameset(I) List]. ∀[K:Cname List]. ∀[x:nameset(I)]. ∀[f:name-morph(I-[x];K)]. ∀[i:ℕ2].
∀[box:open_box(c𝕌;I;J;x;i)].
(cu_filler_1{i:l}(I;J;K;f;x;i;box) ∈ Type)
Proof
Definitions occuring in Statement :
cu_filler_1: cu_filler_1{i:l}(I;J;K;f;x;i;box),
cubical-universe: c𝕌,
open_box: open_box(X;I;J;x;i),
name-morph: name-morph(I;J),
nameset: nameset(L),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
cons: [a / b],
nil: [],
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q,
or: P ∨ Q,
sq_exists: ∃x:{A| B[x]},
cu_filler_1: cu_filler_1{i:l}(I;J;K;f;x;i;box),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nameset: nameset(L),
so_lambda: λ2x.t[x],
name-morph: name-morph(I;J),
so_apply: x[s],
uiff: uiff(P;Q),
open_box: open_box(X;I;J;x;i),
prop: ℙ,
guard: {T},
implies: P ⇒ Q,
I-face: I-face(X;I),
face-name: face-name(f),
pi1: fst(t),
pi2: snd(t),
face-cube: cube(f)
Lemmas referenced :
cu-filler-cases,
l-first-when-none,
nameset_wf,
subtype_rel_list,
coordinate_name_wf,
bnot_wf,
isname_wf,
open_box_wf,
cubical-universe_wf,
int_seg_wf,
name-morph_wf,
list-diff_wf,
cname_deq_wf,
cons_wf,
nil_wf,
list_wf,
assert_of_bnot,
not-assert-isname,
get_face_wf,
set_wf,
I-face_wf,
l_member_wf,
equal_wf,
face-name_wf,
nameset_subtype,
list-diff-subset,
subtype_rel_transitivity,
cu-cube-family_wf,
name-comp_wf,
face-map_wf2,
name-morph_subtype,
cu-box-in-box_wf,
fresh-cname_wf,
map_wf,
subtype_rel_dep_function,
l_subset_right_cons_trivial,
subtype_rel_self,
not_wf,
open_box_image_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
unionElimination,
setElimination,
rename,
sqequalRule,
isectElimination,
applyEquality,
independent_isectElimination,
lambdaEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
instantiate,
natural_numberEquality,
productEquality,
cumulativity,
universeEquality,
independent_pairEquality,
lambdaFormation,
independent_functionElimination,
setEquality,
functionExtensionality
Latex:
\mforall{}[I:Cname List]. \mforall{}[J:nameset(I) List]. \mforall{}[K:Cname List]. \mforall{}[x:nameset(I)]. \mforall{}[f:name-morph(I-[x];K)].
\mforall{}[i:\mBbbN{}2]. \mforall{}[box:open\_box(c\mBbbU{};I;J;x;i)].
(cu\_filler\_1\{i:l\}(I;J;K;f;x;i;box) \mmember{} Type)
Date html generated:
2017_10_05-PM-04_14_20
Last ObjectModification:
2017_07_28-AM-11_30_30
Theory : cubical!sets
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