Nuprl Lemma : sub_ps_context_weakening
∀[C:SmallCategory]. ∀[X,Z:ps_context{j:l}(C)]. sub_ps_context{j:l}(C; Z; X) supposing Z = X ∈ ps_context{j:l}(C)
Proof
Definitions occuring in Statement :
sub_ps_context: Y ⊆ X,
ps_context: __⊢,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sub_ps_context: Y ⊆ X,
subtype_rel: A ⊆r B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
cat-ob: cat-ob(C),
pi1: fst(t),
op-cat: op-cat(C),
spreadn: spread4,
cat-arrow: cat-arrow(C),
pi2: snd(t),
type-cat: TypeCat,
all: ∀x:A. B[x],
cat-comp: cat-comp(C),
compose: f o g
Lemmas referenced :
pscm-id_wf,
small-category-cumulativity-2,
ps_context_cumulativity2,
subtype_rel_self,
psc_map_wf,
sub_ps_context_wf,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
sqequalRule,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalityIstype,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X,Z:ps\_context\{j:l\}(C)]. sub\_ps\_context\{j:l\}(C; Z; X) supposing Z = X
Date html generated:
2020_05_20-PM-01_24_46
Last ObjectModification:
2020_04_01-AM-09_55_24
Theory : presheaf!models!of!type!theory
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