Nuprl Lemma : cubical-type-iso_wf
∀[X:j⊢]. (cubical-type-iso(X) ∈ cubical_type{i:l}(X) ⟶ {X ⊢' _})
Proof
Definitions occuring in Statement :
cubical-type-iso: cubical-type-iso(X),
cubical-type: {X ⊢ _},
cubical_type: cubical_type{i:l}(X),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cubical_type: cubical_type{i:l}(X),
presheaf_type: presheaf_type{i:l}(C; X),
cubes: cubes(X),
cubical-type-iso: cubical-type-iso(X),
presheaf-type-iso: presheaf-type-iso(X),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
presheaf-type-iso_wf,
cube-cat_wf,
cubical-type-sq-presheaf-type
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
instantiate,
Error :memTop
Latex:
\mforall{}[X:j\mvdash{}]. (cubical-type-iso(X) \mmember{} cubical\_type\{i:l\}(X) {}\mrightarrow{} \{X \mvdash{}' \_\})
Date html generated:
2020_05_20-PM-01_46_35
Last ObjectModification:
2020_04_03-PM-07_58_00
Theory : cubical!type!theory
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