Nuprl Lemma : context-map-comp2
∀[G:j⊢]. ∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[a:G(I)]. (<a> o <f> = <f(a)> ∈ formal-cube(J) ij⟶ G)
Proof
Definitions occuring in Statement :
csm-comp: G o F,
context-map: <rho>,
cube_set_map: A ⟶ B,
formal-cube: formal-cube(I),
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
cube_set_map: A ⟶ B,
formal-cube: formal-cube(I),
Yoneda: Yoneda(I),
csm-comp: G o F,
pscm-comp: G o F,
context-map: <rho>,
ps-context-map: <rho>,
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
ps-context-map-comp2,
cube-cat_wf,
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
cat_comp_tuple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
dependent_functionElimination,
Error :memTop
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[a:G(I)]. (<a> o <f> = <f(a)>)
Date html generated:
2020_05_20-PM-01_54_00
Last ObjectModification:
2020_04_04-AM-09_33_26
Theory : cubical!type!theory
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