Nuprl Lemma : bag-filter-singleton
∀[T:Type]. ∀[p:T ⟶ 𝔹]. ∀[v:T]. ([x∈{v}|p[x]] ~ if p[v] then {v} else {} fi )
Proof
Definitions occuring in Statement :
bag-filter: [x∈b|p[x]],
single-bag: {x},
empty-bag: {},
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
empty-bag: {},
single-bag: {x},
bag-filter: [x∈b|p[x]],
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
filter_cons_lemma,
filter_nil_lemma,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
hypothesisEquality,
isectElimination,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[p:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[v:T]. ([x\mmember{}\{v\}|p[x]] \msim{} if p[v] then \{v\} else \{\} fi )
Date html generated:
2016_05_15-PM-02_23_16
Last ObjectModification:
2015_12_27-AM-09_54_19
Theory : bags
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