Nuprl Lemma : pscm-comp-assoc
∀[C:SmallCategory]. ∀[A,B,E,D:ps_context{j:l}(C)]. ∀[F:psc_map{j:l}(C; A; B)]. ∀[G:psc_map{j:l}(C; B; E)].
∀[H:psc_map{j:l}(C; E; D)].
(H o G o F = H o G o F ∈ psc_map{j:l}(C; A; D))
Proof
Definitions occuring in Statement :
pscm-comp: G o F,
psc_map: A ⟶ B,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
psc_map: A ⟶ B,
ps_context: __⊢,
all: ∀x:A. B[x]
Lemmas referenced :
pscm-comp-sq,
psc_map_wf,
small-category_wf,
trans-comp-assoc,
op-cat_wf,
type-cat_wf,
small-category-cumulativity-2
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
universeIsType,
instantiate,
applyEquality,
because_Cache,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
Error :memTop,
dependent_functionElimination
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[A,B,E,D:ps\_context\{j:l\}(C)]. \mforall{}[F:psc\_map\{j:l\}(C; A; B)]. \mforall{}[G:psc\_map\{j:l\}(C;
B;
E)].
\mforall{}[H:psc\_map\{j:l\}(C; E; D)].
(H o G o F = H o G o F)
Date html generated:
2020_05_20-PM-01_24_09
Last ObjectModification:
2020_04_01-AM-10_53_33
Theory : presheaf!models!of!type!theory
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