Nuprl Lemma : csm-comp-assoc
∀[A,B,C,D:j⊢]. ∀[F:A j⟶ B]. ∀[G:B j⟶ C]. ∀[H:C j⟶ D]. (H o G o F = H o G o F ∈ A j⟶ 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,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
csm-comp: G o F,
pscm-comp: G o F
Lemmas referenced :
pscm-comp-assoc,
cube-cat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule
Latex:
\mforall{}[A,B,C,D:j\mvdash{}]. \mforall{}[F:A j{}\mrightarrow{} B]. \mforall{}[G:B j{}\mrightarrow{} C]. \mforall{}[H:C j{}\mrightarrow{} D]. (H o G o F = H o G o F)
Date html generated:
2020_05_20-PM-01_41_44
Last ObjectModification:
2020_04_03-PM-03_33_53
Theory : cubical!type!theory
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