Nuprl Lemma : subset-comp-structure
∀[X,Y:j⊢]. ∀[T:{Y ⊢ _}]. Y ⊢ Compositon(T) ⊆r X ⊢ Compositon(T) supposing sub_cubical_set{j:l}(X; Y)
Proof
Definitions occuring in Statement :
composition-structure: Gamma ⊢ Compositon(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]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
composition-structure-subset,
sub_cubical_set_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
axiomEquality,
universeIsType,
instantiate,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X,Y:j\mvdash{}]. \mforall{}[T:\{Y \mvdash{} \_\}].
Y \mvdash{} Compositon(T) \msubseteq{}r X \mvdash{} Compositon(T) supposing sub\_cubical\_set\{j:l\}(X; Y)
Date html generated:
2020_05_20-PM-04_36_33
Last ObjectModification:
2020_04_19-PM-01_54_18
Theory : cubical!type!theory
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