Nuprl Lemma : discrete-cubical-term-at-morph
∀[T:Type]. ∀[X:j⊢]. ∀[t:{X ⊢ _:discr(T)}]. ∀I,J:fset(ℕ). ∀f:J ⟶ I. ∀a:X(I). (t(a) = t(f(a)) ∈ T)
Proof
Definitions occuring in Statement :
discrete-cubical-type: discr(T),
cubical-term-at: u(a),
cubical-term: {X ⊢ _:A},
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
discrete-cubical-type: discr(T),
discrete-presheaf-type: discr(T),
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
cubical-term-at: u(a),
presheaf-term-at: u(a),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
discrete-presheaf-term-at-morph,
cube-cat_wf,
cubical-term-sq-presheaf-term,
cat_ob_pair_lemma,
cat_arrow_triple_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{}[T:Type]. \mforall{}[X:j\mvdash{}]. \mforall{}[t:\{X \mvdash{} \_:discr(T)\}]. \mforall{}I,J:fset(\mBbbN{}). \mforall{}f:J {}\mrightarrow{} I. \mforall{}a:X(I). (t(a) = t(f(a)))
Date html generated:
2020_05_20-PM-02_31_29
Last ObjectModification:
2020_04_03-PM-08_41_51
Theory : cubical!type!theory
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