Nuprl Lemma : cc-adjoin-cube_wf
∀X:CubicalSet. ∀A:{X ⊢ _}. ∀J:Cname List. ∀v:X(J). ∀u:A(v). ((v;u) ∈ X.A(J))
Proof
Definitions occuring in Statement :
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
I-cube: X(I),
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
cubical-type: {X ⊢ _},
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
I-cube: X(I),
top: Top,
functor-ob: ob(F),
cubical-type-at: A(a),
pi1: fst(t),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
ob_pair_lemma,
subtype_rel_self,
list_wf,
coordinate_name_wf,
cubical-type-at_wf,
name-morph_wf,
I-cube_wf,
cube-set-restriction_wf,
all_wf,
equal_wf,
id-morph_wf,
subtype_rel-equal,
squash_wf,
true_wf,
cube-set-restriction-id,
iff_weakening_equal,
name-comp_wf,
cube-set-restriction-comp,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
dependent_pairEquality,
hypothesisEquality,
applyEquality,
isectElimination,
functionExtensionality,
dependent_set_memberEquality,
functionEquality,
productEquality,
lambdaEquality,
because_Cache,
independent_isectElimination,
instantiate,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}X:CubicalSet. \mforall{}A:\{X \mvdash{} \_\}. \mforall{}J:Cname List. \mforall{}v:X(J). \mforall{}u:A(v). ((v;u) \mmember{} X.A(J))
Date html generated:
2017_10_05-AM-10_13_21
Last ObjectModification:
2017_07_28-AM-11_18_51
Theory : cubical!sets
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