Nuprl Lemma : cubical-path_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[a,b:{X ⊢ _:A}]. ∀[I:Cname List]. ∀[alpha:X(I)]. (cubical-path(X;A;a;b;I;alpha) ∈ Type)
Proof
Definitions occuring in Statement :
cubical-path: cubical-path(X;A;a;b;I;alpha),
cubical-term: {X ⊢ _:AF},
cubical-type: {X ⊢ _},
I-cube: X(I),
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-path: cubical-path(X;A;a;b;I;alpha),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
quotient_wf,
I-path_wf,
path-eq_wf,
path-eq-equiv,
I-cube_wf,
list_wf,
coordinate_name_wf,
cubical-term_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[a,b:\{X \mvdash{} \_:A\}]. \mforall{}[I:Cname List]. \mforall{}[alpha:X(I)].
(cubical-path(X;A;a;b;I;alpha) \mmember{} Type)
Date html generated:
2016_06_16-PM-07_30_17
Last ObjectModification:
2015_12_28-PM-04_12_56
Theory : cubical!sets
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