Nuprl Lemma : discrete-cubical-term_wf
∀[T:Type]. ∀[t:T]. ∀[X:CubicalSet].  (discr(t) ∈ {X ⊢ _:discr(T)})
Proof
Definitions occuring in Statement : 
discrete-cubical-term: discr(t)
, 
discrete-cubical-type: discr(T)
, 
cubical-term: {X ⊢ _:AF}
, 
cubical-set: CubicalSet
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
discrete-cubical-term: discr(t)
, 
discrete-cubical-type: discr(T)
, 
cubical-term: {X ⊢ _:AF}
, 
pi1: fst(t)
, 
all: ∀x:A. B[x]
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
implies: P 
⇒ Q
, 
top: Top
, 
prop: ℙ
, 
so_apply: x[s]
Lemmas referenced : 
I-cube_wf, 
list_wf, 
coordinate_name_wf, 
name-morph_wf, 
all_wf, 
equal_wf, 
cube-set-restriction_wf, 
top_wf, 
pi1_wf_top, 
cubical-set_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
dependent_set_memberEquality, 
sqequalRule, 
lambdaEquality, 
hypothesisEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
lambdaFormation, 
because_Cache, 
cumulativity, 
applyEquality, 
functionExtensionality, 
independent_pairEquality, 
isect_memberEquality, 
universeEquality, 
productEquality, 
functionEquality, 
isectEquality, 
instantiate, 
productElimination, 
voidElimination, 
voidEquality, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
axiomEquality
Latex:
\mforall{}[T:Type].  \mforall{}[t:T].  \mforall{}[X:CubicalSet].    (discr(t)  \mmember{}  \{X  \mvdash{}  \_:discr(T)\})
Date html generated:
2017_10_05-AM-10_17_19
Last ObjectModification:
2017_07_28-AM-11_20_15
Theory : cubical!sets
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