Nuprl Lemma : interleaving_occurence_wf
∀[T:Type]. ∀[L1,L2,L:T List]. ∀[f1:ℕ||L1|| ⟶ ℕ||L||]. ∀[f2:ℕ||L2|| ⟶ ℕ||L||].
(interleaving_occurence(T;L1;L2;L;f1;f2) ∈ ℙ)
Proof
Definitions occuring in Statement :
interleaving_occurence: interleaving_occurence(T;L1;L2;L;f1;f2),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
interleaving_occurence: interleaving_occurence(T;L1;L2;L;f1;f2),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
so_apply: x[s]
Lemmas referenced :
equal_wf,
nat_wf,
length_wf_nat,
length_wf,
add_nat_wf,
nat_properties,
decidable__le,
add-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_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_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
false_wf,
le_wf,
increasing_wf,
int_seg_wf,
all_wf,
select_wf,
int_seg_properties,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
non_neg_length,
lelt_wf,
not_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
cumulativity,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
because_Cache,
functionExtensionality,
applyEquality,
imageElimination,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2,L:T List]. \mforall{}[f1:\mBbbN{}||L1|| {}\mrightarrow{} \mBbbN{}||L||]. \mforall{}[f2:\mBbbN{}||L2|| {}\mrightarrow{} \mBbbN{}||L||].
(interleaving\_occurence(T;L1;L2;L;f1;f2) \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-08_37_19
Last ObjectModification:
2017_07_26-PM-04_26_27
Theory : list!
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