Nuprl Lemma : context-map-subset
∀[G:j⊢]. ∀[phi:{G ⊢ _:𝔽}]. ∀[I:fset(ℕ)]. ∀[a:G, phi(I)]. (<a> = <a> ∈ formal-cube(I) j⟶ G, phi)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
context-map: <rho>,
cube_set_map: A ⟶ B,
formal-cube: formal-cube(I),
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
context-subset: Gamma, phi,
context-map: <rho>,
all: ∀x:A. B[x],
member: t ∈ T,
functor-arrow: arrow(F),
cube-set-restriction: f(s),
csm-ap: (s)x,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
arrow_pair_lemma,
csm-ap_wf,
formal-cube_wf1,
context-subset_wf,
cubical_set_cumulativity-i-j,
context-map_wf,
I_cube_wf,
csm-equal,
fset_wf,
nat_wf,
cubical-term_wf,
face-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
functionExtensionality,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
instantiate,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
universeIsType
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[phi:\{G \mvdash{} \_:\mBbbF{}\}]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[a:G, phi(I)]. (<a> = <a>)
Date html generated:
2020_05_20-PM-02_45_18
Last ObjectModification:
2020_04_05-PM-01_44_40
Theory : cubical!type!theory
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