Nuprl Lemma : only-bag-map
∀[f:Top]. ∀[T:Type]. ∀[b:bag(T)]. only(bag-map(f;b)) ~ f only(b) supposing #(b) = 1 ∈ ℤ
Proof
Definitions occuring in Statement :
bag-only: only(bs),
bag-size: #(bs),
bag-map: bag-map(f;bs),
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
natural_number: $n,
int: ℤ,
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
single-bag: {x},
bag-only: only(bs),
bag-map: bag-map(f;bs),
top: Top
Lemmas referenced :
bag-size-one,
bag-only_wf,
equal_wf,
equal-wf-T-base,
bag-size_wf,
nat_wf,
bag_wf,
top_wf,
map_cons_lemma,
map_nil_lemma,
reduce_hd_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
cumulativity,
because_Cache,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
sqequalAxiom,
intEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
baseClosed,
isect_memberEquality,
universeEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[f:Top]. \mforall{}[T:Type]. \mforall{}[b:bag(T)]. only(bag-map(f;b)) \msim{} f only(b) supposing \#(b) = 1
Date html generated:
2017_10_01-AM-08_52_37
Last ObjectModification:
2017_07_26-PM-04_34_07
Theory : bags
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