Nuprl Lemma : subset-I_cube
∀[X,Y:j⊢]. ∀I:fset(ℕ). (Y(I) ⊆r X(I)) supposing sub_cubical_set{j:l}(Y; X)
Proof
Definitions occuring in Statement :
sub_cubical_set: Y ⊆ X,
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
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)
Lemmas referenced :
subset-I_set,
cube-cat_wf,
cat_ob_pair_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:fset(\mBbbN{}). (Y(I) \msubseteq{}r X(I)) supposing sub\_cubical\_set\{j:l\}(Y; X)
Date html generated:
2020_05_20-PM-01_43_38
Last ObjectModification:
2020_04_03-PM-04_09_57
Theory : cubical!type!theory
Home
Index