Nuprl Lemma : cubical_sets_equal
∀[X,Y:j⊢].
X = Y ∈ CubicalSet{j} supposing X = Y ∈ (F:fset(ℕ) ⟶ 𝕌{j'} × (x:fset(ℕ) ⟶ y:fset(ℕ) ⟶ y ⟶ x ⟶ (F x) ⟶ (F y)))
Proof
Definitions occuring in Statement :
cubical_set: CubicalSet,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
product: 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,
cube-cat: CubeCat,
all: ∀x:A. B[x]
Lemmas referenced :
ps_contexts_equal,
cube-cat_wf,
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,
dependent_functionElimination,
Error :memTop
Latex:
\mforall{}[X,Y:j\mvdash{}]. X = Y supposing X = Y
Date html generated:
2020_05_20-PM-01_38_45
Last ObjectModification:
2020_04_03-PM-03_42_10
Theory : cubical!type!theory
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