Nuprl Lemma : cubical-refl-app-snd
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[a:{X ⊢ _:A}]. ((refl(a))p @ q = (a)p ∈ {X.𝕀 ⊢ _:(A)p})
Proof
Definitions occuring in Statement :
cubical-refl: refl(a),
cubical-path-app: pth @ r,
interval-type: 𝕀,
cc-snd: q,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
cubical-refl: refl(a),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
term-to-path-app-snd,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
cubical-term_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
thin,
instantiate,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
universeIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[a:\{X \mvdash{} \_:A\}]. ((refl(a))p @ q = (a)p)
Date html generated:
2020_05_20-PM-03_22_10
Last ObjectModification:
2020_04_06-PM-06_39_40
Theory : cubical!type!theory
Home
Index