Nuprl Lemma : context-subset-1-subtype
∀[Gamma:j⊢]. ({Gamma, 1(𝔽) ⊢ _} ⊆r {Gamma ⊢ _})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-1: 1(𝔽),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
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 :
subset-cubical-type,
context-subset_wf,
face-1_wf,
context-1-subset,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
instantiate,
because_Cache,
sqequalRule,
axiomEquality,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. (\{Gamma, 1(\mBbbF{}) \mvdash{} \_\} \msubseteq{}r \{Gamma \mvdash{} \_\})
Date html generated:
2020_05_20-PM-02_54_28
Last ObjectModification:
2020_04_04-PM-05_08_55
Theory : cubical!type!theory
Home
Index