Nuprl Lemma : context-map-comp
∀[I,J,K:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[g:K ⟶ J]. (<f ⋅ g> = <f> o <g> ∈ formal-cube(K) ⟶ formal-cube(I))
Proof
Definitions occuring in Statement :
csm-comp: G o F,
context-map: <rho>,
cube_set_map: A ⟶ B,
formal-cube: formal-cube(I),
nh-comp: g ⋅ f,
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,
cube-cat: CubeCat,
all: ∀x:A. B[x],
cube_set_map: A ⟶ B,
formal-cube: formal-cube(I),
Yoneda: Yoneda(I),
context-map: <rho>,
ps-context-map: <rho>,
csm-comp: G o F,
pscm-comp: G o F
Lemmas referenced :
ps-ps-context-map-comp,
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{}[I,J,K:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[g:K {}\mrightarrow{} J]. (<f \mcdot{} g> = <f> o <g>)
Date html generated:
2020_05_20-PM-01_42_15
Last ObjectModification:
2020_04_03-PM-04_01_11
Theory : cubical!type!theory
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