Nuprl Lemma : discrete-cat_wf
∀[X:Type]. (discrete-cat(X) ∈ SmallCategory)
Proof
Definitions occuring in Statement :
discrete-cat: discrete-cat(X),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
discrete-cat: discrete-cat(X),
so_lambda: λ2x y.t[x; y],
prop: ℙ,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
unit: Unit,
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
uimplies: b supposing a,
implies: P ⇒ Q,
so_apply: x[s1;s2;s3;s4;s5],
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
it: ⋅
Lemmas referenced :
mk-cat_wf,
equal_wf,
it_wf,
member_wf,
equal-wf-base,
equal_subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
hypothesis,
applyEquality,
equalityElimination,
axiomEquality,
intEquality,
natural_numberEquality,
baseClosed,
independent_isectElimination,
lambdaFormation,
equalityTransitivity,
independent_pairFormation,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[X:Type]. (discrete-cat(X) \mmember{} SmallCategory)
Date html generated:
2017_10_05-AM-00_45_35
Last ObjectModification:
2017_07_28-AM-09_18_57
Theory : small!categories
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