Nuprl Lemma : discrete-presheaf-type_wf
∀[C:SmallCategory]. ∀[T:Type]. ∀[X:ps_context{j:l}(C)]. (discr(T) ∈ X ⊢ )
Proof
Definitions occuring in Statement :
discrete-presheaf-type: discr(T),
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 ⊢ _},
discrete-presheaf-type: discr(T),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
I_set_wf,
cat-ob_wf,
cat-arrow_wf,
psc-restriction_wf,
cat-id_wf,
subtype_rel-equal,
equal_wf,
squash_wf,
true_wf,
istype-universe,
psc-restriction-id,
subtype_rel_self,
iff_weakening_equal,
cat-comp_wf,
psc-restriction-comp,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
lambdaEquality_alt,
hypothesisEquality,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
because_Cache,
applyEquality,
inhabitedIsType,
functionIsType,
lambdaFormation_alt,
independent_pairFormation,
productElimination,
productIsType,
equalityIstype,
independent_isectElimination,
instantiate,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
dependent_functionElimination,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[T:Type]. \mforall{}[X:ps\_context\{j:l\}(C)]. (discr(T) \mmember{} X \mvdash{} )
Date html generated:
2020_05_20-PM-01_34_07
Last ObjectModification:
2020_04_02-PM-06_32_56
Theory : presheaf!models!of!type!theory
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