Nuprl Lemma : psc_map_cumulativity
∀[C:SmallCategory]. ∀[G,H:ps_context{j:l}(C)]. (psc_map{j:l}(C; H; G) ⊆r psc_map{j':l}(C; H; G))
Proof
Definitions occuring in Statement :
psc_map: A ⟶ B,
ps_context: __⊢,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
small-category: SmallCategory,
ps_context: __⊢,
cat-functor: Functor(C1;C2),
functor-ob: ob(F),
type-cat: TypeCat,
op-cat: op-cat(C),
spreadn: spread4,
all: ∀x:A. B[x],
pi1: fst(t),
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
cat_arrow_triple_lemma,
cat_comp_tuple_lemma,
arrow_pair_lemma,
cat_ob_pair_lemma,
cat_id_tuple_lemma,
equal_wf,
squash_wf,
true_wf,
compose_wf,
subtype_rel_self,
iff_weakening_equal,
psc_map_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaEquality_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
productElimination,
dependent_set_memberEquality_alt,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
hypothesisEquality,
lambdaFormation_alt,
applyEquality,
instantiate,
imageElimination,
isectElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType,
because_Cache,
functionEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination,
functionIsType,
equalityIstype
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[G,H:ps\_context\{j:l\}(C)]. (psc\_map\{j:l\}(C; H; G) \msubseteq{}r psc\_map\{j':l\}(C; H; G))
Date html generated:
2020_05_20-PM-01_23_51
Last ObjectModification:
2020_04_16-PM-05_34_06
Theory : presheaf!models!of!type!theory
Home
Index