Nuprl Lemma : filter-commutes
∀[T:Type]. ∀[P1,P2:T ⟶ 𝔹]. ∀[L:T List]. (filter(P1;filter(P2;L)) ~ filter(P2;filter(P1;L)))
Proof
Definitions occuring in Statement :
filter: filter(P;l),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
swap-filter-filter,
list_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P1,P2:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[L:T List]. (filter(P1;filter(P2;L)) \msim{} filter(P2;filter(P1;L)))
Date html generated:
2016_05_15-PM-03_40_17
Last ObjectModification:
2015_12_27-PM-01_16_42
Theory : general
Home
Index