Nuprl Lemma : l_disjoint-concat
∀[T:Type]. ∀[LL:T List List]. ∀[L:T List]. uiff(l_disjoint(T;L;concat(LL));(∀l2∈LL.l_disjoint(T;L;l2)))
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
l_all: (∀x∈L.P[x]),
concat: concat(ll),
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
concat: concat(ll),
all: ∀x:A. B[x],
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_disjoint: l_disjoint(T;l1;l2),
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
less_than: a < b,
squash: ↓T
Lemmas referenced :
list_induction,
list_wf,
uall_wf,
uiff_wf,
l_disjoint_wf,
concat_wf,
l_all_wf,
l_member_wf,
reduce_nil_lemma,
l_disjoint_nil_iff,
nil_wf,
true_wf,
iff_weakening_uiff,
l_all_wf_nil,
l_all_nil_iff,
select_wf,
length_of_nil_lemma,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf,
length_wf,
append_wf,
l_disjoint_append,
concat-cons,
l_all_cons,
cons_wf,
length_of_cons_lemma,
add-is-int-iff,
itermAdd_wf,
int_term_value_add_lemma,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
addLevel,
productElimination,
independent_isectElimination,
cumulativity,
productEquality,
applyEquality,
universeEquality,
unionElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
intEquality,
lambdaFormation,
independent_pairEquality,
imageElimination,
addEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed
Latex:
\mforall{}[T:Type]. \mforall{}[LL:T List List]. \mforall{}[L:T List].
uiff(l\_disjoint(T;L;concat(LL));(\mforall{}l2\mmember{}LL.l\_disjoint(T;L;l2)))
Date html generated:
2019_06_20-PM-01_44_54
Last ObjectModification:
2018_08_24-PM-11_18_05
Theory : list_1
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