Nuprl Lemma : cubical-type-ap-morph_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ∀[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: X(I),
cubical-set: CubicalSet,
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-type-ap-morph: (u a f),
cubical-type: {X ⊢ _},
cubical-type-at: A(a),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
cubical-type-at_wf,
I-cube_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. \mforall{}[a:X(I)]. \mforall{}[u:A(a)].
((u a f) \mmember{} A(f(a)))
Date html generated:
2016_06_16-PM-05_38_53
Last ObjectModification:
2015_12_28-PM-04_36_24
Theory : cubical!sets
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