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:
2020_05_20-AM-07_52_44
Last ObjectModification:
2017_10_03-PM-02_38_54
Theory : small!categories
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