Nuprl Lemma : cube-set-map-is
∀[A,B:j⊢].
(A j⟶ B ~ {trans:I:fset(ℕ) ⟶ A(I) ⟶ B(I)|
∀I,J:fset(ℕ). ∀g:J ⟶ I. ((λs.g(trans I s)) = (λs.(trans J g(s))) ∈ (A(I) ⟶ B(J)))} )
Proof
Definitions occuring in Statement :
cube_set_map: A ⟶ B,
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],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
sqequal: s ~ t,
equal: s = t ∈ T
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),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
psc-map-is,
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{}[A,B:j\mvdash{}].
(A j{}\mrightarrow{} B \msim{} \{trans:I:fset(\mBbbN{}) {}\mrightarrow{} A(I) {}\mrightarrow{} B(I)|
\mforall{}I,J:fset(\mBbbN{}). \mforall{}g:J {}\mrightarrow{} I. ((\mlambda{}s.g(trans I s)) = (\mlambda{}s.(trans J g(s))))\} )
Date html generated:
2020_05_20-PM-01_42_46
Last ObjectModification:
2020_04_03-PM-03_34_35
Theory : cubical!type!theory
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