Nuprl Lemma : sv-bag-only-map2
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[b:bag(A)].
(sv-bag-only(bag-map(f;b)) = (f sv-bag-only(b)) ∈ B) supposing (0 < #(b) and single-valued-bag(b;A))
Proof
Definitions occuring in Statement :
sv-bag-only: sv-bag-only(b),
single-valued-bag: single-valued-bag(b;T),
bag-size: #(bs),
bag-map: bag-map(f;bs),
bag: bag(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
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,
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
sv-bag-only-map,
less_than_wf,
bag-size_wf,
nat_wf,
single-valued-bag_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
natural_numberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[b:bag(A)].
(sv-bag-only(bag-map(f;b)) = (f sv-bag-only(b))) supposing (0 < \#(b) and single-valued-bag(b;A))
Date html generated:
2016_05_15-PM-02_44_09
Last ObjectModification:
2015_12_27-AM-09_38_33
Theory : bags
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