Nuprl Lemma : constant-presheaf-type_wf
∀[C:SmallCategory]. ∀[X:small_ps_context{i:l}(C)]. ∀[Gamma:ps_context{j:l}(C)]. ((X) ∈ Gamma ⊢ )
Proof
Definitions occuring in Statement :
constant-presheaf-type: (X),
presheaf-type: {X ⊢ _},
small_ps_context: small_ps_context{i:l}(C),
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory,
spreadn: spread4,
and: P ∧ Q,
small_ps_context: small_ps_context{i:l}(C),
cat-functor: Functor(C1;C2),
type-cat: TypeCat,
op-cat: op-cat(C),
all: ∀x:A. B[x],
constant-presheaf-type: (X),
presheaf-type: {X ⊢ _},
subtype_rel: A ⊆r B,
cand: A c∧ B,
squash: ↓T,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
compose: f o g,
cat-ob: cat-ob(C),
pi1: fst(t),
cat-arrow: cat-arrow(C),
pi2: snd(t),
cat-id: cat-id(C),
prop: ℙ
Lemmas referenced :
cat_arrow_triple_lemma,
cat_id_tuple_lemma,
cat_comp_tuple_lemma,
cat_ob_pair_lemma,
I_set_pair_redex_lemma,
psc_restriction_pair_lemma,
I_set_wf,
istype-top,
psc-restriction_wf,
equal_wf,
iff_weakening_equal,
subtype_rel-equal,
psc-restriction-when-id,
subtype_rel_self,
cat-arrow_wf,
cat-id_wf,
psc-restriction-comp,
ps_context_wf,
small-category-cumulativity-2,
small_ps_context_wf,
small-category-subtype,
small-category_wf,
squash_wf,
true_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
hypothesisEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
lambdaEquality_alt,
applyEquality,
universeIsType,
isectElimination,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
because_Cache,
functionIsType,
lambdaFormation_alt,
independent_pairFormation,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
productIsType,
equalityIstype,
instantiate,
universeEquality
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:small\_ps\_context\{i:l\}(C)]. \mforall{}[Gamma:ps\_context\{j:l\}(C)]. ((X) \mmember{} Gamma \mvdash{} )
Date html generated:
2020_05_20-PM-01_34_52
Last ObjectModification:
2020_04_03-AM-01_19_06
Theory : presheaf!models!of!type!theory
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