Nuprl Lemma : csm-context-subset-subtype2
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[X:j⊢]. (Gamma j⟶ X ⊆r Gamma, phi j⟶ X)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
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_set_map_subtype3,
context-subset_wf,
sub_cubical_set_self,
context-subset-is-subset,
cubical-term_wf,
face-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,
hypothesis,
because_Cache,
independent_isectElimination,
sqequalRule,
axiomEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[X:j\mvdash{}]. (Gamma j{}\mrightarrow{} X \msubseteq{}r Gamma, phi j{}\mrightarrow{} X)
Date html generated:
2020_05_20-PM-02_59_03
Last ObjectModification:
2020_04_04-PM-05_13_35
Theory : cubical!type!theory
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