Nuprl Lemma : istype-cubical-type-at
∀[X:j⊢]. ∀[I:fset(ℕ)]. ∀[a:X(I)]. ∀[A:{X ⊢ _}]. istype(A(a))
Proof
Definitions occuring in Statement :
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
istype: istype(T),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-type-at_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
cubical-type_wf,
I_cube_wf,
fset_wf,
nat_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
universeIsType,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[a:X(I)]. \mforall{}[A:\{X \mvdash{} \_\}]. istype(A(a))
Date html generated:
2020_05_20-PM-01_47_48
Last ObjectModification:
2020_04_03-PM-08_23_58
Theory : cubical!type!theory
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