Nuprl Lemma : psc-adjoin-set-restriction
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ∀[J,K,g,v,u:Top]. (g((v;u)) ~ (g(v);(u v g)))
Proof
Definitions occuring in Statement :
psc-adjoin-set: (v;u),
psc-adjoin: X.A,
presheaf-type-ap-morph: (u a f),
presheaf-type: {X ⊢ _},
psc-restriction: f(s),
ps_context: __⊢,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf-type: {X ⊢ _},
presheaf-type-ap-morph: (u a f),
psc-adjoin-set: (v;u),
psc-adjoin: X.A,
all: ∀x:A. B[x],
pi2: snd(t),
pi1: fst(t),
psc-restriction: f(s),
subtype_rel: A ⊆r B
Lemmas referenced :
psc_restriction_pair_lemma,
presheaf_type_ap_morph_pair_lemma,
istype-top,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
axiomSqEquality,
inhabitedIsType,
hypothesisEquality,
isect_memberEquality_alt,
isectElimination,
isectIsTypeImplies,
universeIsType,
instantiate,
applyEquality
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[J,K,g,v,u:Top].
(g((v;u)) \msim{} (g(v);(u v g)))
Date html generated:
2020_05_20-PM-01_27_20
Last ObjectModification:
2020_04_02-AM-11_21_10
Theory : presheaf!models!of!type!theory
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