Nuprl Lemma : subset-cubical-term2
∀[X,Y:j⊢]. ∀[A,B:{X ⊢ _}]. {X ⊢ _:A} ⊆r {Y ⊢ _:B} supposing A = B ∈ {X ⊢ _} supposing sub_cubical_set{j:l}(Y; X)
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
sub_cubical_set: Y ⊆ X,
cubical_set: CubicalSet,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
sub_cubical_set: Y ⊆ X,
sub_ps_context: Y ⊆ X,
cube_set_map: A ⟶ B,
csm-id: 1(X),
pscm-id: 1(X)
Lemmas referenced :
subset-presheaf-term2,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cubical-term-sq-presheaf-term
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop
Latex:
\mforall{}[X,Y:j\mvdash{}].
\mforall{}[A,B:\{X \mvdash{} \_\}]. \{X \mvdash{} \_:A\} \msubseteq{}r \{Y \mvdash{} \_:B\} supposing A = B supposing sub\_cubical\_set\{j:l\}(Y; X)
Date html generated:
2020_05_20-PM-02_33_44
Last ObjectModification:
2020_04_03-PM-08_43_59
Theory : cubical!type!theory
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