Nuprl Lemma : csm-context-subset-subtype
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[X:j⊢]. (X j⟶ Gamma, phi.𝕀 ⊆r X j⟶ Gamma.𝕀)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
interval-type: 𝕀,
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
cube_set_map: A ⟶ B,
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 :
cube-context-adjoin_wf,
context-subset_wf,
interval-type_wf,
cube_set_map_subtype3,
sub_cubical_set_functionality,
context-subset-is-subset,
sub_cubical_set_self,
cubical-term_wf,
face-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
because_Cache,
independent_isectElimination,
sqequalRule,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[X:j\mvdash{}]. (X j{}\mrightarrow{} Gamma, phi.\mBbbI{} \msubseteq{}r X j{}\mrightarrow{} Gamma.\mBbbI{})
Date html generated:
2020_05_20-PM-02_58_39
Last ObjectModification:
2020_04_06-AM-11_33_12
Theory : cubical!type!theory
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