Nuprl Lemma : interleaving_sublist
∀[T:Type]. ∀L,L1,L2:T List. (interleaving(T;L1;L2;L) ⇒ L1 ⊆ L)
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
sublist: L1 ⊆ L2,
interleaving: interleaving(T;L1;L2;L),
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
cand: A c∧ B,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
nat: ℕ,
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
so_apply: x[s],
uiff: uiff(P;Q)
Lemmas referenced :
increasing_wf,
length_wf_nat,
int_seg_wf,
length_wf,
all_wf,
equal_wf,
select_wf,
int_seg_properties,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
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_wf,
add_nat_wf,
add-is-int-iff,
itermAdd_wf,
intformeq_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
false_wf,
le_wf,
exists_wf,
not_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
hypothesis,
independent_pairFormation,
productEquality,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
functionExtensionality,
applyEquality,
because_Cache,
natural_numberEquality,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_functionElimination,
unionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageElimination,
dependent_set_memberEquality,
independent_functionElimination,
addEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L,L1,L2:T List. (interleaving(T;L1;L2;L) {}\mRightarrow{} L1 \msubseteq{} L)
Date html generated:
2017_10_01-AM-08_37_15
Last ObjectModification:
2017_07_26-PM-04_26_23
Theory : list!
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