Nuprl Lemma : filter2_functionality
∀[A:Type]. ∀[L:A List]. ∀[f1,f2:ℕ||L|| ⟶ 𝔹].
filter2(f2;L) = filter2(f1;L) ∈ (A List) supposing f1 = f2 ∈ (ℕ||L|| ⟶ 𝔹)
Proof
Definitions occuring in Statement :
filter2: filter2(P;L),
length: ||as||,
list: T List,
int_seg: {i..j-},
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
and_wf,
equal_wf,
int_seg_wf,
length_wf,
bool_wf,
filter2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality,
hypothesis,
independent_pairFormation,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
applyLambdaEquality,
setElimination,
rename,
productElimination,
equalitySymmetry,
universeIsType,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
inhabitedIsType,
because_Cache,
functionIsType,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[L:A List]. \mforall{}[f1,f2:\mBbbN{}||L|| {}\mrightarrow{} \mBbbB{}]. filter2(f2;L) = filter2(f1;L) supposing f1 = f2
Date html generated:
2019_10_15-AM-10_55_07
Last ObjectModification:
2018_09_27-AM-10_45_27
Theory : list!
Home
Index