Nuprl Lemma : single-valued-bag-map
∀[A,B:Type]. ∀[as:bag(A)]. ∀[f:A ⟶ B]. single-valued-bag(bag-map(f;as);B) supposing single-valued-bag(as;A)
Proof
Definitions occuring in Statement :
single-valued-bag: single-valued-bag(b;T),
bag-map: bag-map(f;bs),
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
single-valued-bag: single-valued-bag(b;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
bag-member-map,
and_wf,
equal_wf,
bag-member_wf,
bag-map_wf,
single-valued-bag_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
hypothesis,
productElimination,
independent_isectElimination,
imageElimination,
independent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
axiomEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[as:bag(A)]. \mforall{}[f:A {}\mrightarrow{} B].
single-valued-bag(bag-map(f;as);B) supposing single-valued-bag(as;A)
Date html generated:
2016_05_15-PM-02_42_54
Last ObjectModification:
2015_12_27-AM-09_39_25
Theory : bags
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