Nuprl Lemma : discrete-presheaf-term_wf
∀[C:SmallCategory]. ∀[T:Type]. ∀[t:T]. ∀[X:ps_context{j:l}(C)]. (discr(t) ∈ {X ⊢ _:discr(T)})
Proof
Definitions occuring in Statement :
discrete-presheaf-term: discr(t),
discrete-presheaf-type: discr(T),
presheaf-term: {X ⊢ _:A},
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,
discrete-presheaf-term: discr(t),
discrete-presheaf-type: discr(T),
presheaf-term: {X ⊢ _:A},
presheaf-type-at: A(a),
pi1: fst(t),
presheaf-type-ap-morph: (u a f),
pi2: snd(t),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
I_set_wf,
cat-ob_wf,
cat-arrow_wf,
psc-restriction_wf,
ps_context_wf,
small-category-cumulativity-2,
istype-universe,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
sqequalRule,
lambdaEquality_alt,
hypothesisEquality,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaFormation_alt,
applyEquality,
inhabitedIsType,
functionIsType,
because_Cache,
equalityIstype,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
isect_memberEquality_alt,
isectIsTypeImplies,
universeEquality
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[T:Type]. \mforall{}[t:T]. \mforall{}[X:ps\_context\{j:l\}(C)]. (discr(t) \mmember{} \{X \mvdash{} \_:discr(T)\})
Date html generated:
2020_05_20-PM-01_34_11
Last ObjectModification:
2020_04_02-PM-06_33_06
Theory : presheaf!models!of!type!theory
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