Nuprl Lemma : universe-type_wf
∀[X:j⊢]. ∀[t:{X ⊢ _:c𝕌}]. ∀[I:fset(ℕ)]. ∀[a:X(I)]. formal-cube(I) ⊢ universe-type(t;I;a)
Proof
Definitions occuring in Statement :
universe-type: universe-type(t;I;a),
cubical-universe: c𝕌,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
formal-cube: formal-cube(I),
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
universe-type: universe-type(t;I;a),
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
cubical-universe_wf,
cubical-term-at_wf,
cubical-universe-at,
pi1_wf_top,
cubical-type_wf,
formal-cube_wf1,
I_cube_wf,
fset_wf,
nat_wf,
istype-cubical-universe-term,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
inhabitedIsType,
lambdaFormation_alt,
Error :memTop,
productElimination,
independent_pairEquality,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
universeIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[t:\{X \mvdash{} \_:c\mBbbU{}\}]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[a:X(I)]. formal-cube(I) \mvdash{} universe-type(t;I;a)
Date html generated:
2020_05_20-PM-07_08_14
Last ObjectModification:
2020_04_25-PM-01_32_11
Theory : cubical!type!theory
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