Nuprl Lemma : csm-ap-restriction
∀X,Y:CubicalSet. ∀s:X ⟶ Y. ∀I,J:Cname List. ∀f:name-morph(I;J). ∀a:X(I). (f((s)a) = (s)f(a) ∈ Y(J))
Proof
Definitions occuring in Statement :
cube-set-restriction: f(s),
csm-ap: (s)x,
I-cube: X(I),
cube-set-map: A ⟶ B,
cubical-set: CubicalSet,
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
cubical-set: CubicalSet,
cube-set-map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
I-cube: X(I),
functor-ob: functor-ob(F),
pi1: fst(t),
functor-arrow: functor-arrow(F),
type-cat: TypeCat,
cat-comp: cat-comp(C),
cat-arrow: cat-arrow(C),
name-cat: NameCat,
cat-ob: cat-ob(C),
pi2: snd(t),
compose: f o g,
cube-set-restriction: f(s),
csm-ap: (s)x,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
I-cube_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
cube-set-map_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
lambdaEquality,
functionEquality,
lemma_by_obid,
isectElimination
Latex:
\mforall{}X,Y:CubicalSet. \mforall{}s:X {}\mrightarrow{} Y. \mforall{}I,J:Cname List. \mforall{}f:name-morph(I;J). \mforall{}a:X(I). (f((s)a) = (s)f(a))
Date html generated:
2016_06_16-PM-05_37_36
Last ObjectModification:
2015_12_28-PM-04_37_11
Theory : cubical!sets
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