Nuprl Lemma : cubical-term-equal2
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[u,z:{X ⊢ _:A}]. u = z ∈ {X ⊢ _:A} supposing ∀I:fset(ℕ). ∀a:X(I). ((u I a) = (z I a) ∈ A(a))
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a)
Lemmas referenced :
presheaf-term-equal2,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cubical-term-sq-presheaf-term,
cat_ob_pair_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop,
dependent_functionElimination
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u,z:\{X \mvdash{} \_:A\}]. u = z supposing \mforall{}I:fset(\mBbbN{}). \mforall{}a:X(I). ((u I a) = (z I a))
Date html generated:
2020_05_20-PM-01_52_32
Last ObjectModification:
2020_04_03-PM-08_28_02
Theory : cubical!type!theory
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