Nuprl Lemma : ext-equal-presheaves_wf
∀[C:SmallCategory]. ∀[F,G:Presheaf(C)].  (ext-equal-presheaves(C;F;G) ∈ ℙ')
Proof
Definitions occuring in Statement : 
ext-equal-presheaves: ext-equal-presheaves(C;F;G)
, 
presheaf: Presheaf(C)
, 
small-category: SmallCategory
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
ext-equal-presheaves: ext-equal-presheaves(C;F;G)
, 
prop: ℙ
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
presheaf: Presheaf(C)
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
so_apply: x[s]
, 
top: Top
, 
cat-arrow: cat-arrow(C)
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
type-cat: TypeCat
, 
ext-eq: A ≡ B
Lemmas referenced : 
all_wf, 
cat-ob_wf, 
ext-eq_wf, 
functor-ob_wf, 
op-cat_wf, 
small-category-subtype, 
type-cat_wf, 
subtype_rel-equal, 
cat_ob_op_lemma, 
cat-arrow_wf, 
equal_wf, 
functor-arrow_wf, 
op-cat-arrow, 
subtype_rel_self, 
presheaf_wf, 
small-category_wf, 
cat_arrow_triple_lemma, 
subtype_rel_dep_function
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
productEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
lambdaEquality, 
applyEquality, 
instantiate, 
because_Cache, 
independent_isectElimination, 
dependent_functionElimination, 
cumulativity, 
universeEquality, 
functionEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
lambdaFormation
Latex:
\mforall{}[C:SmallCategory].  \mforall{}[F,G:Presheaf(C)].    (ext-equal-presheaves(C;F;G)  \mmember{}  \mBbbP{}')
Date html generated:
2017_10_05-AM-00_46_54
Last ObjectModification:
2017_10_03-PM-02_38_54
Theory : small!categories
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