Nuprl Lemma : contractibilty-of-singleton
∀X:j⊢. ∀A:{X ⊢ _}. ∀a:{X ⊢ _:A}. {X ⊢ _:Contractible(Singleton(a))}
Proof
Definitions occuring in Statement :
singleton-type: Singleton(a),
contractible-type: Contractible(A),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
singleton-contr_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
cubical-term_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
universeIsType
Latex:
\mforall{}X:j\mvdash{}. \mforall{}A:\{X \mvdash{} \_\}. \mforall{}a:\{X \mvdash{} \_:A\}. \{X \mvdash{} \_:Contractible(Singleton(a))\}
Date html generated:
2020_05_20-PM-03_30_24
Last ObjectModification:
2020_04_06-PM-06_52_32
Theory : cubical!type!theory
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