Nuprl Lemma : contr-center_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[c:{X ⊢ _:Contractible(A)}]. (contr-center(c) ∈ {X ⊢ _:A})
Proof
Definitions occuring in Statement :
contr-center: contr-center(c),
contractible-type: Contractible(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,
contractible-type: Contractible(A),
contr-center: contr-center(c),
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-fst_wf,
cubical-pi_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
csm-ap-type_wf,
cc-fst_wf,
path-type_wf,
csm-ap-term_wf,
cc-snd_wf,
cubical-term_wf,
contractible-type_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
instantiate,
applyEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[c:\{X \mvdash{} \_:Contractible(A)\}]. (contr-center(c) \mmember{} \{X \mvdash{} \_:A\})
Date html generated:
2020_05_20-PM-03_23_03
Last ObjectModification:
2020_04_06-PM-06_39_52
Theory : cubical!type!theory
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