Nuprl Lemma : csm-ap-term-universe
∀[X,H:j⊢]. ∀[s:H j⟶ X]. ∀[t:{X ⊢ _:c𝕌}]. ((t)s ∈ {H ⊢ _:c𝕌})
Proof
Definitions occuring in Statement :
cubical-universe: c𝕌,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
csm-ap-term_wf,
cubical-universe_wf,
csm-cubical-universe,
istype-cubical-universe-term,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
because_Cache,
hypothesis,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
universeIsType,
inhabitedIsType
Latex:
\mforall{}[X,H:j\mvdash{}]. \mforall{}[s:H j{}\mrightarrow{} X]. \mforall{}[t:\{X \mvdash{} \_:c\mBbbU{}\}]. ((t)s \mmember{} \{H \mvdash{} \_:c\mBbbU{}\})
Date html generated:
2020_05_20-PM-07_08_44
Last ObjectModification:
2020_04_28-AM-10_00_36
Theory : cubical!type!theory
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