Nuprl Lemma : cat-id-isomorphism
∀C:SmallCategory. ∀x:cat-ob(C). cat-isomorphism(C;x;x;cat-id(C) x)
Proof
Definitions occuring in Statement :
cat-isomorphism: cat-isomorphism(C;x;y;f),
cat-id: cat-id(C),
cat-ob: cat-ob(C),
small-category: SmallCategory,
all: ∀x:A. B[x],
apply: f a
Definitions unfolded in proof :
all: ∀x:A. B[x],
cat-isomorphism: cat-isomorphism(C;x;y;f),
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
cat-inverse: fg=1,
prop: ℙ
Lemmas referenced :
cat-id_wf,
cat-comp-ident,
cat-inverse_wf,
cat-ob_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
applyEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
productElimination,
independent_pairFormation,
productEquality
Latex:
\mforall{}C:SmallCategory. \mforall{}x:cat-ob(C). cat-isomorphism(C;x;x;cat-id(C) x)
Date html generated:
2020_05_20-AM-07_50_10
Last ObjectModification:
2017_01_08-PM-01_15_23
Theory : small!categories
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