Nuprl Lemma : cube-set-restriction-when-id
∀[X:j⊢]. ∀[I:fset(ℕ)]. ∀[s:X(I)]. ∀[f:I ⟶ I]. f(s) = s ∈ X(I) supposing f = 1 ∈ I ⟶ I
Proof
Definitions occuring in Statement :
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
nh-id: 1,
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,
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-when-id,
cube-cat_wf,
cat_ob_pair_lemma,
cat_arrow_triple_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{}[X:j\mvdash{}]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[s:X(I)]. \mforall{}[f:I {}\mrightarrow{} I]. f(s) = s supposing f = 1
Date html generated:
2020_05_20-PM-01_42_27
Last ObjectModification:
2020_04_03-PM-03_34_21
Theory : cubical!type!theory
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