Nuprl Lemma : sets-ob
∀[C:SmallCategory]. ∀[X:Top]. (cat-ob(sets(C; X)) ~ I:cat-ob(C) × X(I))
Proof
Definitions occuring in Statement :
sets: sets(C; X),
I_set: A(I),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory,
spreadn: spread4,
I_set: A(I),
sets: sets(C; X),
all: ∀x:A. B[x],
top: Top,
presheaf-elements: el(P),
mk-cat: mk-cat,
and: P ∧ Q
Lemmas referenced :
cat_ob_pair_lemma,
cat_ob_op_lemma,
top_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
equalityTransitivity,
equalitySymmetry,
sqequalAxiom,
isectElimination,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:Top]. (cat-ob(sets(C; X)) \msim{} I:cat-ob(C) \mtimes{} X(I))
Date html generated:
2018_05_22-PM-09_59_09
Last ObjectModification:
2018_05_20-PM-09_41_59
Theory : presheaf!models!of!type!theory
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