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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