Nuprl Lemma : cubical-term-at_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[u:{X ⊢ _:A}]. ∀[I:Cname List]. ∀[a:X(I)]. (u(a) ∈ A(a))
Proof
Definitions occuring in Statement :
cubical-term-at: u(a),
cubical-term: {X ⊢ _:AF},
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
I-cube: X(I),
cubical-set: CubicalSet,
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-term-at: u(a),
cubical-type-at: A(a),
cubical-term: {X ⊢ _:AF}
Lemmas referenced :
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,
applyEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u:\{X \mvdash{} \_:A\}]. \mforall{}[I:Cname List]. \mforall{}[a:X(I)]. (u(a) \mmember{} A(a))
Date html generated:
2016_06_16-PM-05_40_06
Last ObjectModification:
2015_12_28-PM-04_35_44
Theory : cubical!sets
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