Nuprl Lemma : poset-cat-arrow-unique
∀[I:Cname List]. ∀[x,y:cat-ob(poset-cat(I))]. ∀[a,b:cat-arrow(poset-cat(I)) x y].
(a = b ∈ (cat-arrow(poset-cat(I)) x y))
Proof
Definitions occuring in Statement :
poset-cat: poset-cat(J),
coordinate_name: Cname,
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
list: T List,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
poset-cat: poset-cat(J),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
assert: ↑b,
prop: ℙ,
false: False,
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
bfalse: ff,
true: True
Lemmas referenced :
assert_wf,
le_int_wf,
equal_wf,
nameset_wf,
extd-nameset_subtype_int,
nil_wf,
coordinate_name_wf,
name-morph_wf,
list_wf,
bnot_wf,
not_wf,
le_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
applyEquality,
hypothesisEquality,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
hypothesis,
because_Cache,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
isect_memberEquality,
axiomEquality,
voidElimination,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
productElimination,
independent_pairFormation,
impliesFunctionality,
equalityElimination
Latex:
\mforall{}[I:Cname List]. \mforall{}[x,y:cat-ob(poset-cat(I))]. \mforall{}[a,b:cat-arrow(poset-cat(I)) x y]. (a = b)
Date html generated:
2016_06_16-PM-06_52_24
Last ObjectModification:
2015_12_28-PM-04_22_55
Theory : cubical!sets
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