Nuprl Lemma : bag-combine-unit-left
∀[A,B:Type]. ∀[f:A ⟶ bag(B)]. ∀[a:A]. (⋃x∈[a].f[x] ~ f[a])
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
bag: bag(T),
cons: [a / b],
nil: [],
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,
bag-combine: ⋃x∈bs.f[x],
bag-map: bag-map(f;bs),
bag-union: bag-union(bbs),
all: ∀x:A. B[x],
top: Top,
concat: concat(ll),
empty-bag: {},
bag-append: as + bs,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
map_cons_lemma,
map_nil_lemma,
reduce_cons_lemma,
reduce_nil_lemma,
bag-append-empty,
bag-subtype-list,
bag_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,
isectElimination,
applyEquality,
hypothesisEquality,
sqequalAxiom,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. \mforall{}[a:A]. (\mcup{}x\mmember{}[a].f[x] \msim{} f[a])
Date html generated:
2016_05_15-PM-02_28_12
Last ObjectModification:
2015_12_27-AM-09_50_50
Theory : bags
Home
Index