Nuprl Lemma : presheaf-term_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ({X ⊢ _:A} ∈ 𝕌{[i | j']})
Proof
Definitions occuring in Statement :
presheaf-term: {X ⊢ _:A},
presheaf-type: {X ⊢ _},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf-type: {X ⊢ _},
presheaf-term: {X ⊢ _:A},
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
presheaf_type_at_pair_lemma,
presheaf_type_ap_morph_pair_lemma,
cat-ob_wf,
I_set_wf,
cat-arrow_wf,
equal_wf,
psc-restriction_wf,
small-category-cumulativity-2,
ps_context_cumulativity2,
presheaf-type_wf,
ps_context_wf,
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,
setEquality,
functionEquality,
cumulativity,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. (\{X \mvdash{} \_:A\} \mmember{} \mBbbU{}\{[i | j']\})
Date html generated:
2020_05_20-PM-01_26_32
Last ObjectModification:
2020_03_31-PM-02_39_26
Theory : presheaf!models!of!type!theory
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