Nuprl Lemma : discrete-path-equal
∀[T:Type]. ∀[X:j⊢]. ∀[a,b:{X ⊢ _:discr(T)}]. ∀[p1,p2:{X ⊢ _:(Path_discr(T) a b)}].
(p1 = p2 ∈ {X ⊢ _:(Path_discr(T) a b)})
Proof
Definitions occuring in Statement :
path-type: (Path_A a b),
discrete-cubical-type: discr(T),
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
discrete-path,
cubical-term_wf,
path-type_wf,
discrete-cubical-type_wf,
cubical_set_wf,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeIsType,
instantiate,
cumulativity,
inhabitedIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[X:j\mvdash{}]. \mforall{}[a,b:\{X \mvdash{} \_:discr(T)\}]. \mforall{}[p1,p2:\{X \mvdash{} \_:(Path\_discr(T) a b)\}]. (p1 = p2)
Date html generated:
2020_05_20-PM-03_37_03
Last ObjectModification:
2020_04_06-PM-07_03_16
Theory : cubical!type!theory
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