Nuprl Lemma : discrete-groupoid_wf
∀[X:Type]. (discrete-groupoid(X) ∈ Groupoid)
Proof
Definitions occuring in Statement :
discrete-groupoid: discrete-groupoid(X),
groupoid: Groupoid,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
discrete-groupoid: discrete-groupoid(X),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
cat-comp: cat-comp(C),
pi2: snd(t),
discrete-cat: discrete-cat(X),
mk-cat: mk-cat,
it: ⋅,
cat-id: cat-id(C),
pi1: fst(t),
top: Top,
subtype_rel: A ⊆r B,
unit: Unit,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
mk-groupoid_wf,
discrete-cat_wf,
cat-arrow_wf,
cat-ob_wf,
cat-id_wf,
cat_arrow_triple_lemma,
cat_ob_pair_lemma,
it_wf,
equal_subtype,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
intEquality,
natural_numberEquality,
baseClosed
Latex:
\mforall{}[X:Type]. (discrete-groupoid(X) \mmember{} Groupoid)
Date html generated:
2017_01_19-PM-02_56_04
Last ObjectModification:
2017_01_13-PM-00_14_38
Theory : small!categories
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