Nuprl Lemma : discrete-map-is-constant
∀[T:𝕌{j}]. ∀[I:fset(ℕ)]. ∀[s:formal-cube(I) ij⟶ discrete-cube(T)].
(s = (λJ,g. (s I 1)) ∈ formal-cube(I) ij⟶ discrete-cube(T))
Proof
Definitions occuring in Statement :
cube_set_map: A ⟶ B,
discrete-cube: discrete-cube(A),
formal-cube: formal-cube(I),
nh-id: 1,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cube-cat: CubeCat,
all: ∀x:A. B[x],
cube_set_map: A ⟶ B,
formal-cube: formal-cube(I),
Yoneda: Yoneda(I),
discrete-cube: discrete-cube(A),
discrete-set: discrete-set(A)
Lemmas referenced :
ps-discrete-map-is-constant,
cube-cat_wf,
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
cat_comp_tuple_lemma,
cat_id_tuple_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{}[T:\mBbbU{}\{j\}]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[s:formal-cube(I) ij{}\mrightarrow{} discrete-cube(T)]. (s = (\mlambda{}J,g. (s I 1)))
Date html generated:
2020_05_20-PM-02_31_55
Last ObjectModification:
2020_04_04-AM-09_47_57
Theory : cubical!type!theory
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