Nuprl Lemma : cubical-type-ap-morph_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[a:X(I)]. ∀[u:A(a)]. ((u a f) ∈ A(f(a)))
Proof
Definitions occuring in Statement :
cubical-type-ap-morph: (u a f),
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
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-type: {X ⊢ _},
cubical-type-ap-morph: (u a f),
all: ∀x:A. B[x],
pi2: snd(t),
cubical-type-at: A(a),
pi1: fst(t)
Lemmas referenced :
cubical_type_at_pair_lemma,
istype-cubical-type-at,
I_cube_wf,
names-hom_wf,
fset_wf,
nat_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
applyEquality,
hypothesisEquality,
isectElimination,
universeIsType,
because_Cache,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[a:X(I)]. \mforall{}[u:A(a)]. ((u a f) \mmember{} A(f(a)))
Date html generated:
2020_05_20-PM-01_47_57
Last ObjectModification:
2020_04_06-PM-11_38_34
Theory : cubical!type!theory
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