Nuprl Lemma : cube-set-restriction_wf
∀[X:j⊢]. ∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[s:X(I)]. (f(s) ∈ X(J))
Proof
Definitions occuring in Statement :
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: 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],
I_cube: A(I),
I_set: A(I),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
psc-restriction_wf,
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:j\mvdash{}]. \mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[s:X(I)]. (f(s) \mmember{} X(J))
Date html generated:
2020_05_20-PM-01_39_02
Last ObjectModification:
2020_04_03-PM-03_32_41
Theory : cubical!type!theory
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