Nuprl Lemma : refl-map_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. (refl-map(X;A) ∈ {X ⊢ _:(A ⟶ discr({X.A ⊢ _:Path((A)p)}))})
Proof
Definitions occuring in Statement :
refl-map: refl-map(X;A),
pathtype: Path(A),
discrete-cubical-type: discr(T),
cubical-fun: (A ⟶ B),
cc-fst: p,
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
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,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
refl-map: refl-map(X;A)
Lemmas referenced :
cubical-refl_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
csm-ap-type_wf,
cc-fst_wf,
cc-snd_wf,
path-type-subtype,
csm-discrete-cubical-type,
discrete-cubical-term_wf,
pathtype_wf,
cubical-term-eqcd,
cubical-lam_wf,
discrete-cubical-type_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
universeIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. (refl-map(X;A) \mmember{} \{X \mvdash{} \_:(A {}\mrightarrow{} discr(\{X.A \mvdash{} \_:Path((A)p)\}))\})
Date html generated:
2020_05_20-PM-03_44_18
Last ObjectModification:
2020_04_20-PM-07_30_45
Theory : cubical!type!theory
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