Nuprl Lemma : discrete-path
∀[T:Type]. ∀[X:j⊢]. ∀[a,b:{X ⊢ _:discr(T)}]. ∀[p:{X ⊢ _:(Path_discr(T) a b)}].
(p = refl(a) ∈ {X ⊢ _:(Path_discr(T) a b)})
Proof
Definitions occuring in Statement :
cubical-refl: refl(a),
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,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
discrete-pathtype,
path-type-subtype,
discrete-cubical-type_wf,
cubical-term_wf,
path-type_wf,
cubical_set_wf,
istype-universe,
cubical-path-app-0,
equal_wf,
pathtype_wf,
cubical-refl_wf,
paths-equal
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
universeIsType,
instantiate,
cumulativity,
because_Cache,
universeEquality,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
equalityTransitivity,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[X:j\mvdash{}]. \mforall{}[a,b:\{X \mvdash{} \_:discr(T)\}]. \mforall{}[p:\{X \mvdash{} \_:(Path\_discr(T) a b)\}]. (p = refl(a))
Date html generated:
2020_05_20-PM-03_36_51
Last ObjectModification:
2020_04_07-PM-04_28_20
Theory : cubical!type!theory
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