Nuprl Lemma : Kan-groupoid-nerve_wf
∀[G:Groupoid]. (Kan-groupoid-nerve(G) ∈ KanCubicalSet)
Proof
Definitions occuring in Statement :
Kan-groupoid-nerve: Kan-groupoid-nerve(G),
Kan-cubical-set: KanCubicalSet,
groupoid: Groupoid,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Kan-cubical-set: KanCubicalSet,
Kan-groupoid-nerve: Kan-groupoid-nerve(G),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nameset: nameset(L),
and: P ∧ Q,
cand: A c∧ B,
Kan-filler: Kan-filler(X;filler),
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
cubical-nerve_wf,
groupoid-cat_wf,
groupoid-nerve-filler_wf,
open_box_wf,
subtype_rel_list,
nameset_wf,
coordinate_name_wf,
int_seg_wf,
list_wf,
I-cube_wf,
groupoid-nerve-filler-fills,
groupoid-nerve-filler-uniform,
and_wf,
Kan-filler_wf,
uniform-Kan-filler_wf,
groupoid_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
applyEquality,
independent_isectElimination,
setElimination,
rename,
sqequalRule,
natural_numberEquality,
functionEquality,
lambdaFormation,
dependent_functionElimination,
independent_pairFormation,
spreadEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[G:Groupoid]. (Kan-groupoid-nerve(G) \mmember{} KanCubicalSet)
Date html generated:
2016_06_16-PM-07_27_15
Last ObjectModification:
2015_12_28-PM-04_14_41
Theory : cubical!sets
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