Nuprl Lemma : interleaving_implies_occurence
∀[T:Type]
∀L1,L2,L:T List.
(interleaving(T;L1;L2;L) ⇒ (∃f1:ℕ||L1|| ⟶ ℕ||L||. ∃f2:ℕ||L2|| ⟶ ℕ||L||. interleaving_occurence(T;L1;L2;L;f1;f2)))
Proof
Definitions occuring in Statement :
interleaving_occurence: interleaving_occurence(T;L1;L2;L;f1;f2),
interleaving: interleaving(T;L1;L2;L),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
interleaving: interleaving(T;L1;L2;L),
interleaving_occurence: interleaving_occurence(T;L1;L2;L;f1;f2),
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
and: P ∧ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
true: True,
prop: ℙ,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
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]
Lemmas referenced :
equal_wf,
nat_wf,
increasing_wf,
length_wf_nat,
int_seg_wf,
length_wf,
all_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,
not_wf,
exists_wf,
interleaving_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
sqequalRule,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
natural_numberEquality,
independent_pairFormation,
hypothesis,
productEquality,
introduction,
extract_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
cumulativity,
functionExtensionality,
applyEquality,
lambdaEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
applyLambdaEquality,
dependent_functionElimination,
unionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageElimination,
dependent_set_memberEquality,
independent_functionElimination,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}L1,L2,L:T List.
(interleaving(T;L1;L2;L)
{}\mRightarrow{} (\mexists{}f1:\mBbbN{}||L1|| {}\mrightarrow{} \mBbbN{}||L||. \mexists{}f2:\mBbbN{}||L2|| {}\mrightarrow{} \mBbbN{}||L||. interleaving\_occurence(T;L1;L2;L;f1;f2)))
Date html generated:
2017_10_01-AM-08_37_21
Last ObjectModification:
2017_07_26-PM-04_26_29
Theory : list!
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