Nuprl Lemma : disjoint_sublists_sublist
∀[T:Type]. ∀L1,L2,L:T List. (disjoint_sublists(T;L1;L2;L) ⇒ {L1 ⊆ L ∧ L2 ⊆ L})
Proof
Definitions occuring in Statement :
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
sublist: L1 ⊆ L2,
guard: {T},
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
increasing_wf,
length_wf_nat,
int_seg_wf,
length_wf,
all_wf,
equal_wf,
select_wf,
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,
non_neg_length,
lelt_wf,
nat_properties,
disjoint_sublists_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
dependent_pairFormation,
hypothesisEquality,
independent_pairFormation,
hypothesis,
productEquality,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
functionExtensionality,
applyEquality,
because_Cache,
sqequalRule,
natural_numberEquality,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2,L:T List. (disjoint\_sublists(T;L1;L2;L) {}\mRightarrow{} \{L1 \msubseteq{} L \mwedge{} L2 \msubseteq{} L\})
Date html generated:
2018_05_21-PM-06_20_26
Last ObjectModification:
2018_05_19-PM-05_32_40
Theory : list!
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