Nuprl Lemma : sub_cubical_set_functionality
∀[Y,X:j⊢]. ∀[A:{X ⊢ _}]. sub_cubical_set{[i | j]:l}(Y.A; X.A) supposing sub_cubical_set{j:l}(Y; X)
Proof
Definitions occuring in Statement :
cube-context-adjoin: X.A,
cubical-type: {X ⊢ _},
sub_cubical_set: Y ⊆ X,
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
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),
cube-context-adjoin: X.A,
psc-adjoin: X.A,
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a),
cube-set-restriction: f(s),
psc-restriction: f(s),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f)
Lemmas referenced :
sub_ps_context_functionality,
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,
Error :memTop
Latex:
\mforall{}[Y,X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. sub\_cubical\_set\{[i | j]:l\}(Y.A; X.A) supposing sub\_cubical\_set\{j:l\}(Y; X)
Date html generated:
2020_05_20-PM-02_34_21
Last ObjectModification:
2020_04_04-AM-09_22_18
Theory : cubical!type!theory
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