Nuprl Lemma : poset-cat_wf
∀[J:Cname List]. (poset-cat(J) ∈ SmallCategory)
Proof
Definitions occuring in Statement :
poset-cat: poset-cat(J),
coordinate_name: Cname,
small-category: SmallCategory,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
poset-cat: poset-cat(J),
small-category: SmallCategory,
so_lambda: λ2x.t[x],
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
nameset: nameset(L),
sq_stable: SqStable(P),
squash: ↓T,
coordinate_name: Cname,
int_upper: {i...},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
le: A ≤ B,
spreadn: spread4,
cand: A c∧ B,
assert: ↑b,
sq_type: SQType(T),
guard: {T},
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
true: True
Lemmas referenced :
list_wf,
coordinate_name_wf,
name-morph_wf,
nil_wf,
all_wf,
nameset_wf,
assert_wf,
le_int_wf,
extd-nameset_subtype_int,
assert_witness,
assert_of_le_int,
sq_stable__l_member,
decidable__equal-coordinate_name,
sq_stable__le,
decidable__le,
le_wf,
l_member_wf,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
intformand_wf,
int_formula_prop_and_lemma,
equal_wf,
bnot_wf,
not_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
dependent_pairEquality,
hypothesisEquality,
lambdaEquality,
applyEquality,
setElimination,
rename,
because_Cache,
independent_pairEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
lambdaFormation,
imageMemberEquality,
baseClosed,
imageElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_pairFormation,
productEquality,
functionEquality,
functionExtensionality,
cumulativity,
universeEquality,
instantiate,
impliesFunctionality,
equalityElimination
Latex:
\mforall{}[J:Cname List]. (poset-cat(J) \mmember{} SmallCategory)
Date html generated:
2017_10_05-AM-10_27_42
Last ObjectModification:
2017_07_28-AM-11_23_15
Theory : cubical!sets
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