Nuprl Lemma : discrete-set_wf
∀[C:SmallCategory]. ∀[A:𝕌{j}]. (discrete-set(A) ∈ ps_context{j:l}(C))
Proof
Definitions occuring in Statement :
discrete-set: discrete-set(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,
ext-eq: A ≡ B,
and: P ∧ Q,
discrete-set: discrete-set(A),
all: ∀x:A. B[x],
psc-restriction: f(s),
pi2: snd(t),
subtype_rel: A ⊆r B
Lemmas referenced :
ps_context-ext,
cat-ob_wf,
cat-arrow_wf,
I_set_pair_redex_lemma,
psc_restriction_pair_lemma,
cat-id_wf,
cat-comp_wf,
istype-universe,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
sqequalRule,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
lambdaEquality_alt,
cumulativity,
universeIsType,
hypothesis,
applyEquality,
inhabitedIsType,
because_Cache,
functionIsType,
dependent_functionElimination,
Error :memTop,
independent_pairFormation,
lambdaFormation_alt,
productIsType,
equalityIstype,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[A:\mBbbU{}\{j\}]. (discrete-set(A) \mmember{} ps\_context\{j:l\}(C))
Date html generated:
2020_05_20-PM-01_23_44
Last ObjectModification:
2020_03_31-PM-07_35_54
Theory : presheaf!models!of!type!theory
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