Nuprl Lemma : bag-map_wf
∀[B,A:Type]. ∀[f:A ⟶ B]. ∀[bs:bag(A)]. (bag-map(f;bs) ∈ bag(B))
Proof
Definitions occuring in Statement :
bag-map: bag-map(f;bs),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
bag: bag(T),
member: t ∈ T,
uall: ∀[x:A]. B[x],
quotient: x,y:A//B[x; y],
and: P ∧ Q,
bag-map: bag-map(f;bs),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
bag_wf,
quotient-member-eq,
list_wf,
permutation_wf,
permutation-equiv,
map_wf,
permutation-map,
equal-wf-base
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
pointwiseFunctionalityForEquality,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
productEquality,
because_Cache,
cumulativity,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[bs:bag(A)]. (bag-map(f;bs) \mmember{} bag(B))
Date html generated:
2016_05_15-PM-02_22_00
Last ObjectModification:
2015_12_27-AM-09_55_15
Theory : bags
Home
Index