Nuprl Lemma : cube-cat_wf
CubeCat ∈ SmallCategory
Proof
Definitions occuring in Statement :
cube-cat: CubeCat,
small-category: SmallCategory,
member: t ∈ T
Definitions unfolded in proof :
cube-cat: CubeCat,
member: t ∈ T,
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
spreadn: spread4,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fset_wf,
nat_wf,
names-hom_wf,
nh-id_wf,
nh-comp_wf,
nh-id-left,
equal_wf,
squash_wf,
true_wf,
nh-id-right,
subtype_rel_self,
iff_weakening_equal,
nh-comp-assoc,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality,
dependent_pairEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
because_Cache,
independent_pairEquality,
sqequalRule,
productEquality,
functionEquality,
applyEquality,
functionExtensionality,
cumulativity,
universeEquality,
lambdaFormation,
dependent_functionElimination,
independent_pairFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
CubeCat \mmember{} SmallCategory
Date html generated:
2018_05_23-AM-08_29_01
Last ObjectModification:
2018_05_20-PM-05_39_37
Theory : cubical!type!theory
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