Nuprl Lemma : psc_map_subtype3
∀[C:SmallCategory]. ∀[X,Y,Z,U:ps_context{j:l}(C)].
(psc_map{j:l}(C; X; Z) ⊆r psc_map{j:l}(C; Y; U)) supposing
(sub_ps_context{j:l}(C; Y; X) and
sub_ps_context{j:l}(C; Z; U))
Proof
Definitions occuring in Statement :
sub_ps_context: Y ⊆ X,
psc_map: A ⟶ B,
ps_context: __⊢,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_transitivity,
psc_map_wf,
psc_map_subtype,
psc_map_subtype2,
sub_ps_context_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
independent_isectElimination,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X,Y,Z,U:ps\_context\{j:l\}(C)].
(psc\_map\{j:l\}(C; X; Z) \msubseteq{}r psc\_map\{j:l\}(C; Y; U)) supposing
(sub\_ps\_context\{j:l\}(C; Y; X) and
sub\_ps\_context\{j:l\}(C; Z; U))
Date html generated:
2020_05_20-PM-01_25_09
Last ObjectModification:
2020_04_01-PM-00_01_27
Theory : presheaf!models!of!type!theory
Home
Index