Nuprl Lemma : cubical-set-is-functor
CubicalSet ≡ Functor(NameCat;TypeCat)
Proof
Definitions occuring in Statement :
cubical-set: CubicalSet,
name-cat: NameCat,
type-cat: TypeCat,
cat-functor: Functor(C1;C2),
ext-eq: A ≡ B
Definitions unfolded in proof :
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
cubical-set: CubicalSet,
cat-functor: Functor(C1;C2),
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
name-cat: NameCat,
cat-ob: cat-ob(C),
pi1: fst(t),
pi2: snd(t),
uall: ∀[x:A]. B[x],
cat-comp: cat-comp(C),
cat-id: cat-id(C),
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
type-cat_wf,
name-cat_wf,
cat-functor_wf,
cubical-set_wf,
compose_wf,
name-comp_wf,
equal_wf,
id-morph_wf,
equal-wf-T-base,
all_wf,
name-morph_wf,
coordinate_name_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
productElimination,
dependent_set_memberEquality,
sqequalRule,
dependent_pairEquality,
hypothesisEquality,
functionEquality,
lemma_by_obid,
isectElimination,
hypothesis,
applyEquality,
productEquality,
baseClosed,
because_Cache,
cumulativity,
universeEquality,
instantiate
Latex:
CubicalSet \mequiv{} Functor(NameCat;TypeCat)
Date html generated:
2016_06_16-PM-05_35_42
Last ObjectModification:
2016_01_18-PM-04_57_02
Theory : cubical!sets
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