Nuprl Lemma : singleton-center_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[a:{X ⊢ _:A}]. (singleton-center(X;a) ∈ {X ⊢ _:Singleton(a)})
Proof
Definitions occuring in Statement :
singleton-center: singleton-center(X;a),
singleton-type: Singleton(a),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
singleton-type: Singleton(a),
singleton-center: singleton-center(X;a),
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
cubical-pair_wf,
path-type_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
csm-ap-type_wf,
cc-fst_wf,
csm-ap-term_wf,
cc-snd_wf,
cubical-refl_wf,
subset-cubical-term2,
sub_cubical_set_self,
csm-id-adjoin_wf,
path-type-q-id-adjoin,
cubical-term_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[a:\{X \mvdash{} \_:A\}]. (singleton-center(X;a) \mmember{} \{X \mvdash{} \_:Singleton(a)\})
Date html generated:
2020_05_20-PM-03_29_25
Last ObjectModification:
2020_04_06-PM-06_51_19
Theory : cubical!type!theory
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