Nuprl Lemma : subset-restriction
∀[X,Y:j⊢]. ∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[a:Y(I)]. (f(a) = f(a) ∈ X(J)) supposing sub_cubical_set{j:l}(Y; X)
Proof
Definitions occuring in Statement :
sub_cubical_set: Y ⊆ X,
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
sub_cubical_set: Y ⊆ X,
sub_ps_context: Y ⊆ X,
cube_set_map: A ⟶ B,
csm-id: 1(X),
pscm-id: 1(X),
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
ps-subset-restriction,
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{}].
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[a:Y(I)]. (f(a) = f(a)) supposing sub\_cubical\_set\{j:l\}(Y; X)
Date html generated:
2020_05_20-PM-01_43_44
Last ObjectModification:
2020_04_03-PM-04_09_52
Theory : cubical!type!theory
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