Nuprl Lemma : cube-set-map-subtype
∀[A,B:j⊢]. (A j⟶ B ⊆r (I:fset(ℕ) ⟶ A(I) ⟶ B(I)))
Proof
Definitions occuring in Statement :
cube_set_map: A ⟶ B,
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I)
Lemmas referenced :
psc-map-subtype,
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{}[A,B:j\mvdash{}]. (A j{}\mrightarrow{} B \msubseteq{}r (I:fset(\mBbbN{}) {}\mrightarrow{} A(I) {}\mrightarrow{} B(I)))
Date html generated:
2020_05_20-PM-01_41_19
Last ObjectModification:
2020_04_03-PM-03_33_42
Theory : cubical!type!theory
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