Nuprl Lemma : cat-isomorphic-equiv
∀C:SmallCategory. EquivRel(cat-ob(C);x,y.cat-isomorphic(C;x;y))
Proof
Definitions occuring in Statement :
cat-isomorphic: cat-isomorphic(C;x;y),
cat-ob: cat-ob(C),
small-category: SmallCategory,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
cat-ob_wf,
small-category_wf,
cat-isomorphic_weakening,
cat-isomorphic_inversion,
cat-isomorphic_wf,
cat-isomorphic_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}C:SmallCategory. EquivRel(cat-ob(C);x,y.cat-isomorphic(C;x;y))
Date html generated:
2020_05_20-AM-07_50_21
Last ObjectModification:
2017_01_08-PM-01_41_45
Theory : small!categories
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