Nuprl Lemma : sublist_occurence_wf
∀[T:Type]. ∀[L1,L2:T List]. ∀[f:ℕ||L1|| ⟶ ℕ||L2||]. (sublist_occurence(T;L1;L2;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
sublist_occurence: sublist_occurence(T;L1;L2;f),
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 :
sublist_occurence: sublist_occurence(T;L1;L2;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[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],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
nat: ℕ
Lemmas referenced :
list_wf,
le_wf,
nat_properties,
lelt_wf,
non_neg_length,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
select_wf,
equal_wf,
all_wf,
length_wf,
int_seg_wf,
subtype_rel_dep_function,
length_wf_nat,
increasing_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
natural_numberEquality,
lambdaEquality,
because_Cache,
intEquality,
independent_isectElimination,
lambdaFormation,
setElimination,
rename,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
setEquality,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. \mforall{}[f:\mBbbN{}||L1|| {}\mrightarrow{} \mBbbN{}||L2||]. (sublist\_occurence(T;L1;L2;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-01_57_25
Last ObjectModification:
2016_01_15-PM-11_30_41
Theory : list!
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