Nuprl Lemma : csm-comp_wf
∀[A,B,C:CubicalSet]. ∀[F:A ⟶ B]. ∀[G:B ⟶ C]. (G o F ∈ A ⟶ C)
Proof
Definitions occuring in Statement :
csm-comp: G o F,
cube-set-map: A ⟶ B,
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
member: 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,
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-set-is-functor,
trans-comp_wf,
name-cat_wf,
type-cat_wf,
cube-set-map_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
productElimination,
thin,
instantiate,
isectElimination,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B,C:CubicalSet]. \mforall{}[F:A {}\mrightarrow{} B]. \mforall{}[G:B {}\mrightarrow{} C]. (G o F \mmember{} A {}\mrightarrow{} C)
Date html generated:
2016_06_16-PM-05_35_53
Last ObjectModification:
2015_12_28-PM-04_37_54
Theory : cubical!sets
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