Nuprl Lemma : tree-cat_wf
∀[X:Type]. (tree-cat(X) ∈ SmallCategory)
Proof
Definitions occuring in Statement :
tree-cat: tree-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,
tree-cat: tree-cat(X),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda5,
so_apply: x[s1;s2;s3;s4;s5],
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
mk-cat_wf,
unit_wf2,
it_wf,
equal-unit
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
hypothesis,
because_Cache,
independent_isectElimination,
lambdaFormation,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[X:Type]. (tree-cat(X) \mmember{} SmallCategory)
Date html generated:
2020_05_20-AM-07_49_44
Last ObjectModification:
2017_01_13-AM-11_44_37
Theory : small!categories
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