Nuprl Lemma : poset-cat-arrow-equals
∀[I:Cname List]. ∀[x,y:cat-ob(poset-cat(I))]. ∀[a:cat-arrow(poset-cat(I)) x y].
(a = (λx.Ax) ∈ (cat-arrow(poset-cat(I)) x y))
Proof
Definitions occuring in Statement :
poset-cat: poset-cat(J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
equal: s = t ∈ T,
axiom: Ax,
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
poset-cat: poset-cat(J),
cat-arrow: cat-arrow(C),
pi2: snd(t),
pi1: fst(t),
cat-ob: cat-ob(C),
all: ∀x:A. B[x],
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
poset-cat-arrow-unique,
cat-arrow_wf,
poset-cat_wf,
cat-ob_wf,
list_wf,
coordinate_name_wf,
assert_witness,
le_int_wf,
extd-nameset_subtype_int,
nil_wf,
nameset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
applyEquality,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
lambdaEquality_alt,
setElimination,
rename,
because_Cache,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}[I:Cname List]. \mforall{}[x,y:cat-ob(poset-cat(I))]. \mforall{}[a:cat-arrow(poset-cat(I)) x y]. (a = (\mlambda{}x.Ax))
Date html generated:
2020_05_21-AM-10_52_41
Last ObjectModification:
2020_02_07-PM-08_17_03
Theory : cubical!sets
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