Nuprl Lemma : context-adjoin-subset1
∀[H:j⊢]. ∀[phi:{H ⊢ _:𝔽}]. sub_cubical_set{j:l}(H.𝕀, (phi)p; H, phi.𝕀)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
interval-type: 𝕀,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
sub_cubical_set: Y ⊆ X,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
sub_cubical_set: Y ⊆ X
Lemmas referenced :
context-adjoin-subset0,
interval-type_wf,
cubical-term_wf,
face-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[H:j\mvdash{}]. \mforall{}[phi:\{H \mvdash{} \_:\mBbbF{}\}]. sub\_cubical\_set\{j:l\}(H.\mBbbI{}, (phi)p; H, phi.\mBbbI{})
Date html generated:
2020_05_20-PM-03_05_19
Last ObjectModification:
2020_04_13-PM-05_50_30
Theory : cubical!type!theory
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