Nuprl Lemma : cube-set-restriction_wf
∀[X:CubicalSet]. ∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ∀[s:X(I)]. (f(s) ∈ X(J))
Proof
Definitions occuring in Statement :
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,
cube-set-restriction: f(s),
cubical-set: CubicalSet,
pi2: snd(t),
I-cube: X(I),
functor-ob: functor-ob(F),
pi1: fst(t)
Lemmas referenced :
I-cube_wf,
name-morph_wf,
list_wf,
coordinate_name_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{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. \mforall{}[s:X(I)]. (f(s) \mmember{} X(J))
Date html generated:
2016_06_16-PM-05_36_35
Last ObjectModification:
2015_12_28-PM-04_37_24
Theory : cubical!sets
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