Nuprl Lemma : cubical-nerve_wf
∀[X:SmallCategory]. (cubical-nerve(X) ∈ CubicalSet)
Proof
Definitions occuring in Statement :
cubical-nerve: cubical-nerve(X),
cubical-set: CubicalSet,
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
cubical-nerve: cubical-nerve(X),
member: t ∈ T,
cubical-set: CubicalSet,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
compose: f o g,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
small-category_wf,
cat-functor_wf,
poset-cat_wf,
list_wf,
coordinate_name_wf,
name-morph_wf,
functor-comp_wf,
poset-functor_wf,
equal_wf,
squash_wf,
true_wf,
poset-functor-comp,
subtype_rel_self,
iff_weakening_equal,
functor-comp-assoc,
poset-id-functor,
functor-comp-id,
all_wf,
name-comp_wf,
compose_wf,
equal-wf-T-base,
id-morph_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
dependent_set_memberEquality,
sqequalRule,
cut,
introduction,
extract_by_obid,
hypothesis,
dependent_pairEquality,
lambdaEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
functionExtensionality,
because_Cache,
functionEquality,
applyEquality,
lambdaFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
spreadEquality,
productEquality
Latex:
\mforall{}[X:SmallCategory]. (cubical-nerve(X) \mmember{} CubicalSet)
Date html generated:
2018_05_23-PM-06_37_42
Last ObjectModification:
2018_05_20-PM-04_37_31
Theory : cubical!sets
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