Nuprl Lemma : csm-ap_wf
∀[X,Y:CubicalSet]. ∀[s:X ⟶ Y]. ∀[I:Cname List]. ∀[x:X(I)]. ((s)x ∈ Y(I))
Proof
Definitions occuring in Statement :
csm-ap: (s)x,
I-cube: X(I),
cube-set-map: A ⟶ B,
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,
csm-ap: (s)x,
cubical-set: CubicalSet,
I-cube: X(I),
functor-ob: functor-ob(F),
pi1: fst(t),
cube-set-map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
name-cat: NameCat,
cat-ob: cat-ob(C),
pi2: snd(t)
Lemmas referenced :
I-cube_wf,
list_wf,
coordinate_name_wf,
cube-set-map_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X,Y:CubicalSet]. \mforall{}[s:X {}\mrightarrow{} Y]. \mforall{}[I:Cname List]. \mforall{}[x:X(I)]. ((s)x \mmember{} Y(I))
Date html generated:
2016_06_16-PM-05_36_26
Last ObjectModification:
2015_12_28-PM-04_37_33
Theory : cubical!sets
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