Nuprl Lemma : csm-comp-assoc
∀[A,B,C,D:CubicalSet]. ∀[F:A ⟶ B]. ∀[G:B ⟶ C]. ∀[H:C ⟶ D]. (H o G o F = H o G o F ∈ A ⟶ D)
Proof
Definitions occuring in Statement :
csm-comp: G o F,
cube-set-map: A ⟶ B,
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
csm-comp: G o F,
cube-set-map: A ⟶ B,
ext-eq: A ≡ B,
and: P ∧ Q,
squash: ↓T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
cubical-set-is-functor,
equal_wf,
nat-trans_wf,
name-cat_wf,
type-cat_wf,
trans-comp-assoc,
trans-comp_wf,
iff_weakening_equal,
cube-set-map_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
productElimination,
thin,
applyEquality,
instantiate,
lambdaEquality,
imageElimination,
isectElimination,
because_Cache,
hypothesis,
hypothesisEquality,
sqequalRule,
dependent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[A,B,C,D:CubicalSet]. \mforall{}[F:A {}\mrightarrow{} B]. \mforall{}[G:B {}\mrightarrow{} C]. \mforall{}[H:C {}\mrightarrow{} D]. (H o G o F = H o G o F)
Date html generated:
2017_10_05-AM-10_11_16
Last ObjectModification:
2017_07_28-AM-11_17_50
Theory : cubical!sets
Home
Index