Nuprl Lemma : poset-cat-dist_wf
∀[I:Cname List]. ∀[x,y:cat-ob(poset-cat(I))]. (poset-cat-dist(I;x;y) ∈ ℕ)
Proof
Definitions occuring in Statement :
poset-cat-dist: poset-cat-dist(I;x;y),
poset-cat: poset-cat(J),
coordinate_name: Cname,
cat-ob: cat-ob(C),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
poset-cat-dist: poset-cat-dist(I;x;y),
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
cat-ob: cat-ob(C),
pi1: fst(t),
poset-cat: poset-cat(J),
name-morph: name-morph(I;J),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
nameset: nameset(L),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff
Lemmas referenced :
length_wf_nat,
coordinate_name_wf,
filter_wf5,
l_member_wf,
eq_int_wf,
nameset_wf,
extd-nameset_wf,
nil_wf,
all_wf,
assert_wf,
isname_wf,
equal_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
extd-nameset_subtype_int,
cat-ob_wf,
poset-cat_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
applyEquality,
setEquality,
functionEquality,
functionExtensionality,
dependent_set_memberEquality,
natural_numberEquality,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[I:Cname List]. \mforall{}[x,y:cat-ob(poset-cat(I))]. (poset-cat-dist(I;x;y) \mmember{} \mBbbN{})
Date html generated:
2017_10_05-AM-10_28_16
Last ObjectModification:
2017_07_28-AM-11_23_37
Theory : cubical!sets
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