Nuprl Lemma : map-member-wf
∀[A,B:Type]. ∀[L:A List]. ∀[f:{a:A| (a ∈ L)} ⟶ B]. (map(f;L) ∈ B List)
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ
Lemmas referenced :
list-subtype,
map_wf,
l_member_wf,
list_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
setEquality,
hypothesis,
functionEquality,
because_Cache,
universeEquality,
isect_memberFormation,
introduction,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:A List]. \mforall{}[f:\{a:A| (a \mmember{} L)\} {}\mrightarrow{} B]. (map(f;L) \mmember{} B List)
Date html generated:
2016_05_15-PM-02_40_11
Last ObjectModification:
2015_12_27-AM-09_41_36
Theory : bags
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