Nuprl Lemma : psc-adjoin-set_wf
∀C:SmallCategory. ∀X:ps_context{j:l}(C). ∀A:{X ⊢ _}. ∀J:cat-ob(C). ∀v:X(J). ∀u:A(v). ((v;u) ∈ X.A(J))
Proof
Definitions occuring in Statement :
psc-adjoin-set: (v;u),
psc-adjoin: X.A,
presheaf-type-at: A(a),
presheaf-type: {X ⊢ _},
I_set: A(I),
ps_context: __⊢,
all: ∀x:A. B[x],
member: t ∈ T,
cat-ob: cat-ob(C),
small-category: SmallCategory
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
presheaf-type: {X ⊢ _},
psc-adjoin-set: (v;u),
psc-adjoin: X.A,
I_set: A(I),
functor-ob: ob(F),
presheaf-type-at: A(a),
pi1: fst(t),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
ob_pair_lemma,
presheaf_type_at_pair_lemma,
presheaf-type-at_wf,
I_set_wf,
cat-ob_wf,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
dependent_pairEquality_alt,
hypothesisEquality,
universeIsType,
applyEquality,
isectElimination,
instantiate
Latex:
\mforall{}C:SmallCategory. \mforall{}X:ps\_context\{j:l\}(C). \mforall{}A:\{X \mvdash{} \_\}. \mforall{}J:cat-ob(C). \mforall{}v:X(J). \mforall{}u:A(v).
((v;u) \mmember{} X.A(J))
Date html generated:
2020_05_20-PM-01_27_17
Last ObjectModification:
2020_04_02-AM-11_21_02
Theory : presheaf!models!of!type!theory
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