Nuprl Lemma : cubical-term_wf

∀[X:j⊢]. ∀[A:{X ⊢ _}].  ({X ⊢ _:A} ∈ 𝕌{[i | j']})


Proof




Definitions occuring in Statement :  cubical-term: {X ⊢ _:A},  cubical-type: {X ⊢ _},  cubical_set: CubicalSet,  uall: ∀[x:A]. B[x],  member: t ∈ T,  universe: Type
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  cubical-type: {X ⊢ _},  cubical-term: {X ⊢ _:A},  all: ∀x:A. B[x],  prop: ℙ
Lemmas referenced :  cubical_type_at_pair_lemma,  cubical_type_ap_morph_pair_lemma,  fset_wf,  nat_wf,  I_cube_wf,  names-hom_wf,  equal_wf,  cube-set-restriction_wf,  cubical-type_wf,  cubical_set_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation_alt,  cut,  sqequalHypSubstitution,  setElimination,  thin,  rename,  productElimination,  sqequalRule,  introduction,  extract_by_obid,  dependent_functionElimination,  Error :memTop,  hypothesis,  setEquality,  functionEquality,  cumulativity,  isectElimination,  hypothesisEquality,  applyEquality,  universeIsType,  instantiate

Latex:
\mforall{}[X:j\mvdash{}].  \mforall{}[A:\{X  \mvdash{}  \_\}].    (\{X  \mvdash{}  \_:A\}  \mmember{}  \mBbbU{}\{[i  |  j']\})



Date html generated: 2020_05_20-PM-01_51_13
Last ObjectModification: 2020_04_07-PM-00_18_05

Theory : cubical!type!theory


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